أي من العبارات التالية تُعبر عن خاصية التوزيع بشكل صحيح؟

6 \times (1 + 7) = 6 \times 1 + 6 \times 7

Distribution property in multiplication

Understanding Quantum Theory of Electrons in Atoms The goal of this section is to understand the electron orbitals (location of electrons in atoms), their different energies, and other properties. The use of quantum theory provides the best understanding to these topics. This knowledge is a precursor to chemical bonding. As was described previously, electrons in atoms can exist only on discrete energy levels but not between them. It is said that the energy of an electron in an atom is quantized, that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels. The energy levels are labeled with an n value, where n = 1, 2, 3, …. Generally speaking, the energy of an electron in an atom is greater for greater values of n. This number, n, is referred to as the principal quantum number. The principal quantum number defines the location of the energy level. It is essentially the same concept as the n in the Bohr atom description. Another name for the principal quantum number is the shell number. The shells of an atom can be thought of concentric circles radiating out from the nucleus. The electrons that belong to a specific shell are most likely to be found within the corresponding circular area. The further we proceed from the nucleus, the higher the shell number, and so the higher the energy level (Figure 9.4.1). The positively charged protons in the nucleus stabilize the electronic orbitals by electrostatic attraction between the positive charges of the protons and the negative charges of the electrons. So the further away the electron is from the nucleus, the greater the energy it has. This quantum mechanical model for where electrons reside in an atom can be used to look at electronic transitions, the events when an electron moves from one energy level to another. If the transition is to a higher energy level, energy is absorbed, and the energy change has a positive value. To obtain the amount of energy necessary for the transition to a higher energy level, a photon is absorbed by the atom. A transition to a lower energy level involves a release of energy, and the energy change is negative. This process is accompanied by emission of a photon by the atom. The following equation summarizes these relationships and is based on the hydrogen atom: The values nf and ni are the final and initial energy states of the electron. The principal quantum number is one of three quantum numbers used to characterize an orbital. An atomic orbital, which is distinct from an orbit, is a general region in an atom within which an electron is most probable to reside. The quantum mechanical model specifies the probability of finding an electron in the three-dimensional space around the nucleus and is based on solutions of the Schrödinger equation. In addition, the principal quantum number defines the energy of an electron in a hydrogen or hydrogen-like atom or an ion (an atom or an ion with only one electron) and the general region in which discrete energy levels of electrons in a multi-electron atoms and ions are located. Another quantum number is l, the angular momentum quantum number. It is an integer that defines the shape of the orbital, and takes on the values, l = 0, 1, 2, …, n – 1. This means that an orbital with n = 1 can have only one value of l, l = 0, whereas n = 2 permits l = 0 and l = 1, and so on. The principal quantum number defines the general size and energy of the orbital. The l value specifies the shape of the orbital. Orbitals with the same value of l form a subshell. In addition, the greater the angular momentum quantum number, the greater is the angular momentum of an electron at this orbital. Orbitals with l = 0 are called s orbitals (or the s subshells). The value l = 1 corresponds to the p orbitals. For a given n, p orbitals constitute a p subshell (e.g., 3p if n = 3). The orbitals with l = 2 are called the d orbitals, followed by the f-, g-, and h-orbitals for l = 3, 4, 5, and there are higher values we will not consider. There are certain distances from the nucleus at which the probability density of finding an electron located at a particular orbital is zero. In other words, the value of the wavefunction ψ is zero at this distance for this orbital. Such a value of radius r is called a radial node. The number of radial nodes in an orbital is n – l – 1. Consider the examples in Figure 9.4.2. The orbitals depicted are of the s type, thus l = 0 for all of them. It can be seen from the graphs of the probability densities that there are 1 – 0 – 1 = 0 places where the density is zero (nodes) for 1s (n = 1), 2 – 0 – 1 = 1 node for 2s, and 3 – 0 – 1 = 2 nodes for the 3s orbitals. The s subshell electron density distribution is spherical and the p subshell has a dumbbell shape. The d and f orbitals are more complex. These shapes represent the three-dimensional regions within which the electron is likely to be found. Principal quantum number (n) & Orbital angular momentum (l): The Orbital Subshell: https://youtu.be/ms7WR149fAY If an electron has an angular momentum (l ≠ 0), then this vector can point in different directions. In addition, the z component of the angular momentum can have more than one value. This means that if a magnetic field is applied in the z direction, orbitals with different values of the z component of the angular momentum will have different energies resulting from interacting with the field. The magnetic quantum number, called ml, specifies the z component of the angular momentum for a particular orbital. For example, for an s orbital, l = 0, and the only value of ml is zero. For p orbitals, l = 1, and ml can be equal to –1, 0, or +1. Generally speaking, ml can be equal to –l, –(l – 1), …, –1, 0, +1, …, (l – 1), l. The total number of possible orbitals with the same value of l (a subshell) is 2l + 1. Thus, there is one s-orbital for ml = 0, there are three p-orbitals for ml = 1, five d-orbitals for ml = 2, seven f-orbitals for ml = 3, and so forth. The principal quantum number defines the general value of the electronic energy. The angular momentum quantum number determines the shape of the orbital. And the magnetic quantum number specifies orientation of the orbital in space, as can be seen in Figure 9.4.3. Figure 9.4.4 illustrates the energy levels for various orbitals. The number before the orbital name (such as 2s, 3p, and so forth) stands for the principal quantum number, n. The letter in the orbital name defines the subshell with a specific angular momentum quantum number l = 0 for s orbitals, 1 for p orbitals, 2 for d orbitals. Finally, there are more than one possible orbitals for l ≥ 1, each corresponding to a specific value of ml. In the case of a hydrogen atom or a one-electron ion (such as He+, Li2+, and so on), energies of all the orbitals with the same n are the same. This is called a degeneracy, and the energy levels for the same principal quantum number, n, are called degenerate energy levels. However, in atoms with more than one electron, this degeneracy is eliminated by the electron–electron interactions, and orbitals that belong to different subshells have different energies. Orbitals within the same subshell (for example ns, np, nd, nf, such as 2p, 3s) are still degenerate and have the same energy. While the three quantum numbers discussed in the previous paragraphs work well for describing electron orbitals, some experiments showed that they were not sufficient to explain all observed results. It was demonstrated in the 1920s that when hydrogen-line spectra are examined at extremely high resolution, some lines are actually not single peaks but, rather, pairs of closely spaced lines. This is the so-called fine structure of the spectrum, and it implies that there are additional small differences in energies of electrons even when they are located in the same orbital. These observations led Samuel Goudsmit and George Uhlenbeck to propose that electrons have a fourth quantum number. They called this the spin quantum number, or ms. The other three quantum numbers, n, l, and ml, are properties of specific atomic orbitals that also define in what part of the space an electron is most likely to be located. Orbitals are a result of solving the Schrödinger equation for electrons in atoms. The electron spin is a different kind of property. It is a completely quantum phenomenon with no analogues in the classical realm. In addition, it cannot be derived from solving the Schrödinger equation and is not related to the normal spatial coordinates (such as the Cartesian x, y, and z). Electron spin describes an intrinsic electron “rotation” or “spinning.” Each electron acts as a tiny magnet or a tiny rotating object with an angular momentum, even though this rotation cannot be observed in terms of the spatial coordinates. The magnitude of the overall electron spin can only have one value, and an electron can only “spin” in one of two quantized states. One is termed the α state, with the z component of the spin being in the positive direction of the z axis. This corresponds to the spin quantum number ms=12. The other is called the β state, with the z component of the spin being negative and ms=−12. Any electron, regardless of the atomic orbital it is located in, can only have one of those two values of the spin quantum number. The energies of electrons having ms=−12 and ms=12 are different if an external magnetic field is applied. Figure 9.4.5 illustrates this phenomenon. An electron acts like a tiny magnet. Its moment is directed up (in the positive direction of the z axis) for the 12 spin quantum number and down (in the negative z direction) for the spin quantum number of −12. A magnet has a lower energy if its magnetic moment is aligned with the external magnetic field (the left electron) and a higher energy for the magnetic moment being opposite to the applied field. This is why an electron with ms=12 has a slightly lower energy in an external field in the positive z direction, and an electron with ms=−12 has a slightly higher energy in the same field. This is true even for an electron occupying the same orbital in an atom. A spectral line corresponding to a transition for electrons from the same orbital but with different spin quantum numbers has two possible values of energy; thus, the line in the spectrum will show a fine structure splitting. The Pauli Exclusion Principle An electron in an atom is completely described by four quantum numbers: n, l, ml, and ms. The first three quantum numbers define the orbital and the fourth quantum number describes the intrinsic electron property called spin. An Austrian physicist Wolfgang Pauli formulated a general principle that gives the last piece of information that we need to understand the general behavior of electrons in atoms. The Pauli exclusion principle can be formulated as follows: No two electrons in the same atom can have exactly the same set of all the four quantum numbers. What this means is that electrons can share the same orbital (the same set of the quantum numbers n, l, and ml), but only if their spin quantum numbers ms have different values. Since the spin quantum number can only have two values (±12), no more than two electrons can occupy the same orbital (and if two electrons are located in the same orbital, they must have opposite spins). Therefore, any atomic orbital can be populated by only zero, one, or two electrons. The properties and meaning of the quantum numbers of electrons in atoms are briefly

Figure 18-11 represents the amount of energy stored as organic material in each trophic level in an ecosystem. The pyramid shape of the diagram indicates the low percentage of energy transfer from one level to the next. On average, 10 percent of the total energy consumed in one trophic level is incor- porated into the organisms in the next. Why is the percentage of energy transfer so low? One reason is that some of the organisms in a trophic level escape being eaten. They eventually die and become food for decomposers, but the energy contained in their bodies does not pass to a higher trophic level. Even when an organism is eaten, some of the molecules in its body will be in a form that the consumer cannot break down and use. For example, a cougar cannot extract energy from the antlers, hooves, and hair of a deer. Also, the energy used by prey for cellu- lar respiration cannot be used by predators to synthesize new bio- mass. Finally, no transformation or transfer of energy is 100 percent efficient. Every time energy is transformed, such as during the reactions of metabolism, some energy is lost as heat. Limitations of Trophic Levels The low rate of energy transfer between trophic levels explains why ecosystems rarely contain more than a few trophic levels. Because only about 10 percent of the energy available at one trophic level is transferred to the next trophic level, there is not enough energy in the top trophic level to support more levels. Organisms at the lowest trophic level are usually much more abundant than organisms at the highest level. In Africa, for exam- ple, you will see about 1,000 zebras, gazelles, and other herbivores for every lion or leopard you see, and there are far more grasses and shrubs than there are herbivores. Higher trophic levels con- tain less energy, so, they can support fewer individuals.A population is a group of organisms that belong to the same species and live in a particular place at the same time. All of the bass living in a pond during a certain period of time make up a pop- ulation because they are isolated in the pond and do not interact with bass living in other ponds. The boundaries of a population may be imposed by a feature of the environment, such as a lake shore, or they can be arbitrarily chosen to simplify a study of the population. The humans shown in Figure 19-1 are part of the pop- ulation of a city. The properties of populations differ from those of individuals. An individual may be born, it may reproduce, or it may die. A population study focuses on a population as a whole—how many individuals are born, how many die, and so on. Population Size A population’s size is the number of individuals that the population contains. Size is a fundamental and important population property but can be difficult to measure directly. If a population is small and composed of immobile organisms, such as plants, its size can be determined simply by counting individuals. Often, though, individ- uals are too abundant, too widespread, or too mobile to be counted easily, and scientists must estimate the number of individuals in the population. Suppose that a scientist wants to know how many oak trees live in a 10 km2 patch of forest. Instead of searching the entire patch of forest and counting all the oak trees, the scientist could count the trees in a smaller section of the forest, such as a 1 km2 area. The scientist could then use this value to estimate the population of the larger area. SECTION 1 OBJECTIVES ● Describe the main properties that scientists measure when they study populations. ● Compare the three general patterns of population dispersion. ● Identify the measurements used to describe changing populations. ● Compare the three general types of survivorship curves. VOCABULARY population population density dispersion birth rate death rate life expectancy age structure survivorship curve FIGURE 19-1 A population can be widely distributed, as Earth’s human population is, or confined to a small area, as species of fish in a lake are. Copyright © by Holt, Rinehart and Winston. All rights reserved. 382 CHAPTER 19 If the small patch contains 25 oaks, an area 10 times larger would likely contain 10 times as many oak trees. A similar kind of sampling technique might be used to estimate the size of the pop- ulation shown in Figure 19-2. To use this kind of estimate, the sci- entist must assume that the distribution of individuals in the entire population is the same as that in the sampled group. Estimates of population size are based on many such assumptions, so all esti- mates have the potential for error. Population Density Population density measures how crowded a population is. This measurement is always expressed as the number of individuals per unit of area or volume. For example, the population density of humans in the United States is about 30 people per square kilome- ter. Table 19-1 shows the population sizes and densities of humans in several countries in 2003. These estimates are calculated for the total land area. Some areas of a country may be sparsely popu- lated, while other areas are very densely populated. Dispersion A third population property is dispersion (di-SPUHR-zhuhn). Dispersion is the spatial distribution of individuals within the popu- lation. In a clumped distribution, individuals are clustered together. In a uniform distribution, individuals are separated by a fairly con- sistent distance. In a random distribution, each individual’s location is independent of the locations of other individuals in the popula- tion. Figure 19-3 illustrates the three possible patterns of dispersion. Clumped distributions often occur when resources such as food or living space are clumped. Clumped distributions may also occur because of a species’ social behavior, such as when animals gather into herds or flocks. Uniform distributions may result from social behavior in which individuals within the same habitat stay as far away from each other as possible. For example, a bird may locate its nest so as to maximize the distance from the nests of other birds. These migrating wildebeests in East Africa are too numerous and mobile to be counted. Scientists must use sampling methods at several locations to monitor changes in the population size of the animals. FIGURE 19-2 TABLE 19-1 Population Size and Density of Some Countries Population size Population density Country (in millions) (in individuals/km2) China 1,289 135 India 1,069 325 United States 292 30 Russia 146 8 Japan 128 337 Mexico 105 54 Kenya 32 54 Australia 20 3 dispersion from the Latin dis-, meaning “out,” and spargere, meaning “to scatter” Word Roots and Origins Copyright © by Holt, Rinehart and Winston. All rights reserved. POPULATIONS 383 The social interactions of birds called gannets, which are shown in Figure 19-3b, result in a uniform distribution. Each gannet chooses a small nesting area on the coast and defends it from other gannets. In this way, each gannet tries to maximize its distance from all of its neighbors, which causes a uniform distribution of individuals. Few populations are truly randomly dispersed. Rather, they show degrees of clumping or uniformity. The dispersion pattern of a population sometimes depends on the scale at which the popu- lation is observed. The gannets shown in Figure 19-3b are uni- formly distributed on a scale of a few meters. However, if the entire island on which the gannets live is observed, the distribution appears clumped because the birds live only near the shore. POPULATION DYNAMICS All populations are dynamic—they change in size and composition over time. To understand these changes, scientists must know more than the population’s size, density, and dispersion. One important measure is the birth rate, the number of births occur- ring in a period of time. In the United States, for example, there are about 4 million births per year. A second important measure is the death rate, or mortality rate, which is the number of deaths in a

THE BATTLE OF THE PHILIPPINE SEA Occured in the Philippine Sea and Marinas The battle engaged the bulk of thepagan American forces, and prevented the Japanese from reinforcing, their fleet in the •Marianas. •A month after, the Japanese LOST THEIR 4 best aircraft carriers in the Battle of Midway, an island northwest of Pearl "Harbor. 1. The Batle of the Philipine Sea lasted just one day June 19- June 20 1944 3. is also called the "Marianas Turkey Shoot” The Battle of the Coral Sea The Coral Sea is Between New Guinea and Australia The Japanese Were Trying to Attack Australia! The U.S. Navy and the Japanese Navy Fought! Nobody Won! U.S. Was Able to STOP the Attack on Australia! (Victory!) The American fleet defeated the Japanese. American planes bombarded Japanese installation in Manila from the air. Air strikes were also carried out in the Visayas. Battle of Okinawa: Battle Details The attack on Okinawa took heavy toll on both sides of the fighting... The Americans lost 7,373 men killed and 32,056 wounded on land. At sea, the Americans lost 5,000 killed and 4,600 wounded. The Japanese lost 107,000 killed and 7,400 men taken prisoner. The Japanese may have lost another 20,000 dead as a result of American tactics whereby Japanese troops were incinerated where they fought. The Americans also lost 36 ships. 368 ships were also damaged. 763 aircraft were destroyed. The Japanese lost 16 ships sunk and over 4,000 aircraft were lost. battle facts -the japanese launched fierce kamikaze attacks l-arge amouunts of civillian deaths -japanese soldiers using civilians as human shields Americans ended with more triumphs in the battles like in: General MacArthur and the Allies next turned to the Island of Iwo Jima The island was critical to the Allies as a base for an attack on Japan It was called the most heavily defended spot on earth Allied and Japanese forces suffered heavy casualties IWO JIMA American soldiers plant the flag ol the Island of Iwo Jima after their victory Battle of Leyte Gulf "Second Battle of the Philippine Sea". Time: October 23 - 26, 1944 during WW. Location: Leyte Gulf in Philippines (East coast), Philippine islands of Leyte, Samar, and Luzon. Largest naval battle in WWII. Leyte was secured and was liberated from the hands of the Japanese Americans decided to launch their attack in Leyte since the weak side of the Japanese fleet was in Visayas. Heavy bombing at the Leyte beaches cleared the way for the landing in Palo, Leyte. Leading the American troops were General Douglas MacArthur and President Osmeña, who took over after the death of President Quezon in Saranak Lake in New York. the battle for the liberation of manila The commonwealth government capital was transferred from tacloban to Manila. Manila once again became the seat of the national leadership. ON july 4, 1945, general macarthur announced the total liberation of the Philippines • The Commonwealth government capital was transferred from Tacloban to Manila. Manila once again became the seat of the national leadership. On July 4, 1945, General MacArthur announced the total liberation of the Philippines. Americans surprised the Japanese with the landing of troops in Lingayen Gulf in Pangasinan. • The Filipino guerillas had already cleared the area and neutralized many of the Japanese forces. The first target was the UST, which was used by the Japanese as a camp for civilian prisoners of war, and they were able to free them. • More than 1000 POWs from Bataan and Corregidor were also freed from the Bilibid Prisons. • The battle of Manila was recorded as the fiercest urban fighting in the entire Pacific War. WATERLOO DAILY COURIER-NEWSPAPER “PEACE! WAR ENDS; JAPANESE ACCEPT ALLIED TERMS. ON EMPEROR" On August 6, due to persistent refusal of Japan to yield, another atomic bomb was dropped in the shipbuilding city of Nagasaki. On August 15, V-J Day (Victory in Japan), Emperor Hirohito finally admitted defeat and on September 3, 1945 the document of surrender was signed on board of the U.S. battleship Missouri in Tokyo Bay. With the liberation of the Philippines, the Americar troops moved on to finally end the war in Asia. The Japanese cities of Tokyo, Osaka, Nagoya and Kure were bombed. In July 26, the allies demanded surrender but the Japanese continued to hold on to their belief that surrender is a dishonor. Atomic bomb was dropped on the populous city of Hiroshima, 60% of the city was destroyed. It was estimated that there were more than 80 000 people died on the spot and more than 37 000 suffered severe injuries. Today, the HIROSHIMA SHRINE serves as a reminder of th horrors of war and the need to preserve PEACE in the world. THE POSTWAR PHILIPPINE COMMONWEALTH-• Philippine Commonwealth resumed. Osmeña was confronted with a war - ravaged country with no financial resources for PROBLEMS • Poverty • Destruction of Properties • Unemployment • Price Increase • Hoarding • Graft and Corruption HINDRANCES -Rehabilitation of INDUSTRIES COULD NOT BE DONE BECAUSE OF LACK OF FUND -RAILWAYS WERE DESTROYED THAT LED TO SLOW PRODUCTION AND TRANSPORTATION SOLUTION -PCAU (Philippine Civil Affairs Unit) was established by MacArthur to provide emergency relief in areas liberated by the Americans. - It organized food distribution centers. CHALLENGES TO INDEPENDENCE • On April 30, 1946, the Philippine the US President. BIASED AGREEMENTS: Rehabilitation or the Tydings Act of 1946, passed by the US Congress, was approved by Commission • This Act created the US Philippine War Damage The Act also provided for the transfer of $100,000,000 surplus property of the United States to the Philippines. The Philippine Armed Forces received large quantities of valuable military equipment and supplies. BIASED AGREEMENTS: • The United States Congress offered $800 million for post World War Il rebuilding funds if the Bell Trade Act was ratified by the Philippine Congress Parity rights granting U.S. citizens and corporations rights to Philippine natural resources equal to (in parity with) those of Philippine citizens The Philippines used to celebrate its Independence Day on July 4, and not June 12, by virtue of the Truman Proclamation in 1946. In the early 1960s, however, the Philippine Historical Association lobbied to bring back June 12 as our Independence Day. In 1962, President Diosdado Macapagal issued a proclamation to make the change official. DECLARATION OF PHILIPPINE INDEPENDENCE • On July 4, 1946, the Americans granted independence to the Philippines.

Can you create an evaluation using this information PHONETICS VS. PHONOLOGY Whereas phonetics is the study of sounds that occur in language, phonology is the study of how these sounds are organized and how they function in language. It uses the classifications of sounds derived from phonetics to describe and analyze how sounds occur in speech. STRUCTURALIST PHONEMICS STRUCTURALIST PHONEMICS As linguists began to study sounds in fine detail, they recognized increasingly complex aspects of phonetic organization. For example, the sound /p/ appears in different varieties in English. STRUCTURALIST PHONEMICS One of the varieties of /p/ is indicated by [ph]. This sound is produced with an accompanying puff of air called aspiration, as in the words “pill,” and “peace.” Another sound, indicated by [p•], is produced when there is little or no aspiration; this sound occurs in a word like “spill.” A third major variety for the /p/ sound is the unreleased [p– ], which may occur at the end of a word like “stop.” To deal with these variations for the /p/ sound, the structuralists suggested the existence of an abstract unit which they termed a phoneme. STRUCTURALIST PHONEMICS A phoneme was defined by the structuralists as an abstract phonological unit that represents a class of real sounds, termed the allophones of a phoneme. The phoneme /p/ in English, then, is represented by the allophones [ph], [p•], and [p– ]. STRUCTURALISTS: MINIMAL PAIRS How do we know what these abstract units of sound called phonemes are? In order to find the phonemes of a language, the structuralists developed the concept of the minimal pair, defined as any two words that: a) Contain the same number of segments b) Differ in meaning c) Exhibit only one phonetic difference. STRUCTURALISTS: MINIMAL PAIRS In practical terms, phonemes distinguish meanings; and a phoneme can also be defined as the smallest meaning-distinguishing unit of sound. For instance, the words “pin” /pɪn/ and “bin” /bɪn/ mean different things, and the only one difference in these words occurs in the initial sounds. STRUCTURALISTS: MINIMAL PAIRS By using the concept of a minimal pair, we can determine that the three variations of the /p/ sound do not represent three phonemes. Certainly, it is possible to pronounce the word cap with either an aspirated [ph ] or unreleased [p– ]; however, the two forms [kæph ] and [kæp– ] are not a minimal pair, even though they involve different sounds, because they are identical in meaning. STRUCTURALISTS: FREE VARIATION The two forms [kæph ] and [kæp– ] are, therefore, said to exhibit free variation: that is, the pronunciation may vary without signifying a change in meaning. In other words, we may conclude that the unreleased [p– ] and the aspirated [ph ] are not representations of different phonemes in English; they are, in fact, allophones of one phoneme, /p/. STRUCTURALISTS: COMPLEMENTARY DISTRIBUTION When phonemes have more than one allophone in a language, the allophones are said to be in complementary distribution. Complementary distribution means that the allophones of a phoneme occur in different phonetic environments (that is, with different sounds surrounding them). TRANSFORMATIONAL- GENERATIVE PHONOLOGY TRANSFORMATIONAL-GENERATIVE PHONOLOGY Transformational-generative phonology is a relatively recent development in linguistic theory. Chomsky launched Transformational-Generative Grammar in 1957, but the earliest studies within this framework were largely concerned with syntax. A decade later, the first comprehensive transformational-generative treatment of English phonology appeared: Chomsky and Halle’s The Sound Pattern of English (1968). TRANSFORMATIONAL-GENERATIVE PHONOLOGY Transformational-generative phonologists strongly oppose the structuralists’ phonemic level. They replace this level by a series of rules that directly relate underlying representations to observed phonetic representations. The central mechanisms in transformational-generative phonology, then, are underlying representations and phonological rules. PHONOLOGICAL RULES A rule is an operational statement in which some linguistic entity is modified, resulting in a new linguistic entity. Rules may add elements, remove elements, or change elements. By using phonological rules, linguists attempt to demonstrate that there is order in linguistic phenomena and that linguistic patterns are systematic. PHONOLOGICAL DERIVATION A phonological derivation is an operation that begins with an underlying representation and, through the application of a set of specific rules, yields the actual sound the speaker produces. The representation of a phonological rule has the following general appearance. /A/ → [B] / C “A” changes to “B” under condition “C” PHONOLOGICAL RULE – EXAMPLE In most Southern dialects, the word ten is pronounced like the word tin. This is not an isolated fact, for den is pronounced like din and Ben is pronounced like bin, and so on. This very general fact can be represented by the phonological rule: /ɛ/ → [I] / ___ [n] den /dɛn/ → /dIn/ Ben /bɛn/ → /bIn/ ten /tɛn/ → /tIn/ /ɛ/ → [I] / ___ [n] - high - low - tense + front + high - tense + front + sonorant + anterior + coronal - continuant NOTATIONAL DEVICES IN PHONOLOGICAL RULES The statement of phonological rules can be complex, and linguists have developed several notational devices for writing them. Often, the following symbols will be necessary for stating the conditions under which rules apply: # indicates a word boundary + indicates an intraword boundary $ indicates a syllable boundary UNDERLYING REPRESENTATIONS AND RELATED ISSUES The transformational-generative description of phonology relates underlying representations to phonetic representations by rules. This can be represented in a simple example: In English, there are certain pairs of words like sign / signature, and malign / malignant that exhibit a regular alternation in their phonetic representations: [g] is present in the second member of the pairs but absent in the first member. UNDERLYING REPRESENTATIONS AND RELATED ISSUES To explain the relatedness of words such as sign / signature, we could claim that the underlying representation of the segment in all such pairs is /g/ and that a rule operates to delete /g/ before syllable-final nasals. Thus, the rule “/g/ is deleted before syllable-final nasal” would appear formally as: + voice - anterior →∅ ____ [+ nasal] $ - coronal UNDERLYING REPRESENTATIONS AND RELATED ISSUES On the left-hand side of the arrow, we place the features needed to uniquely specify /g/ among the consonants; that is, no other consonant has the features [+ voice], [- anterior], and [- coronal]. The symbols → mean that the sound /g/ changes to nothing or more properly “/g/ is deleted.” The horizontal line following the slash mark refers to the position of /g/ - namely, before a segment that is [+nasal]. Finally, this [+nasal] segment occurs before a syllable boundary, as indicated by $. A less formal way of writing this rule would be: /g/ → / _ [+nasal] $ Notice that this rule also helps describe such alternations as phlegm/phlegmatic and paradigm/paradigmatic. Application Activity: Think of other words in which this rule can be applied. Write the sound segments to prove /g/ is deleted. Another example is the process through which the prefix meaning “not” is added to words. This prefix alternates among the forms /Im/, /In/, and /Iŋ/, depending on the point of articulation of the initial segment of the following word. -If the segment begins in the extreme front part of the mouth (labials), the form is /Im/, as in improper. -If the segment begins in the extreme back part of the mouth (velars), the form is /Iŋ/, as in incomplete. -If the segment begins in the mid-region of the mouth (all other sounds), the form is /In/, as in indecent. *Exceptions:Words beginning with /r/ or /l/. Analyze the Word “in + complete,” for example. /n/ → [ŋ] / __ [k] - continuant - continuant - continuant + sonorant → + sonorant - sonorant + anterior - anterior - strident + coronal - coronal - coronal + tense THE VELAR SOFTENING RULE Still another example of alternation in English is found in pairs of words like “electric / electricity,” in which the segments /k/ and /s/ alternate. /k/ changes to [s] only before non- low, front vowels. THE VELAR SOFTENING RULE /k/ → [s] / __ - continuant + continuant - strident → - sonorant V - anterior + anterior - low - coronal + coronal - back

IDEA OF DISTRIBUTIVE PROPERTY IN SOLVING NUMBER OPERATION QUESTION

Short Quiz in Math 3 multiplies 2-digit by 1-digit numbers using the distributive property

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