What is the Cartesian product?

A set of all possible ordered pairs formed from two or more sets.

A set of all possible combinations formed from two or more sets.

A set of all possible subsets formed from two or more sets.

A set of all possible permutations formed from two or more sets.

What is the Cartesian product of sets A = {1, 2} and B = {a, b, c}?

{(1, a), (1, b), (1, c), (2, a), (2, b), (2, c)}

{(a, 1), (b, 1), (c, 1), (a, 2), (b, 2), (c, 2)}

What is the Cartesian product of sets A = {1, 2} and B = {3, 4}?

{(1, 3), (1, 4), (2, 3), (2, 4)}

{(3, 1), (3, 2), (4, 1), (4, 2)}

Given sets A = {1, 2, 3} and B = {a, b}, what is the Cartesian product A x B?

{(1, a), (1, b), (2, a), (2, b), (3, a), (3, b)}

{(1, a), (1, b), (2, a, b), (3, a, b)}

{(a, 1), (b, 1), (a, 2), (b, 2), (a, 3), (b, 3)}

What is the Cartesian product of sets A = {1, 2, 3} and B = {4, 5}?

{(1, 4), (1, 5), (2, 4), (2, 5), (3, 4), (3, 5)}

{(4, 1), (5, 1), (4, 2), (5, 2), (4, 3), (5, 3)}

{(1, 4), (1, 5), (2, 4, 5), (3, 4, 5)}

The Cartesian product is not defined for these sets.

What is the result of taking the cartesian product of two sets with n and m elements respectively?

The cartesian product will have n x m elements.

The cartesian product will have m - n elements.

The cartesian product will have n - m elements.

The cartesian product will have n + m elements.

What is the cartesian product of an empty set?

The cartesian product with an empty set will result in an empty set.

The cartesian product will contain the elements of the original set.

The cartesian product will contain one empty set.

The cartesian product will be undefined.

What is the cartesian product of two sets with 3 and 4 elements respectively?

The cartesian product will have 12 elements.

The cartesian product will have 7 elements.

The cartesian product will have 2 elements.

The cartesian product will have 10 elements.

What is the cartesian product of a set A with 0 elements and a set B with 5 elements?

The cartesian product will have 0 elements.

The cartesian product will have infinite elements.

The cartesian product will have 5 elements.

The cartesian product will have 10 elements.

What is the cartesian product of a set A with 3 elements and Ø ?

The cartesian product will have 3 elements.

The cartesian product will have infinite elements.

The cartesian product will have 1 element.

Orderd pair and cartesian product

Classification of plants • Plants can be classified as cultivated and wild plants. • Both cultivated and wild plants are very useful to people, animals and the environment. 1. Cultivated plants: • Cultivated plants are plants grown by people for selling. • They can be grown in the field, vegetable garden, home garden and orchard. Classification of plants 2. Wild plants Wild plants are plants that grow on their own outside the garden, orchard or field. They have many uses such as: • Food for people and animals • Shelter • Source of fuel in form of firewood. • Examples include, grasses, msasa, yellow wood, mahogany, mopane Plant Nutrition • The presence of plant nutrients in the soil make them grow well. • The three major plant nutrients are nitrogen, phosphorus and potassium. Sources of plant nutrients • The source for plant nutrients are grouped into organic and inorganic sources. Organic sources of plant nutrients • These are found in nature. • They are natural materials such, decayed plant and animal matter which include: • Animal manure from cattle, sheep, goats, poultry and pigs. • Green manure • Legume crops like beans, peas and groundnuts. • Humus • These material sources may also be called natural fertilizers. Inorganic sources of plant nutrients • These are sources of plant nutrients made by people in industries. They include: • Compound fertilizers like compound A, B, C and D. • These have two or more nutrients. • Straight fertilizers like ammonium nitrate, single super phosphate and urea. • A straight fertilizer supplies a single or more nutrient to the crop. A straight fertilizer A Compound fertilizer Sources of N,P,K • Ammonium nitrate and Urea- contain nitrogen Double super Phosphate, Single super phosphate-contain phosphorus • Muriate of Potash contains Potassium 2 . Compound fertilisers -have two or three of the three major plant nutrients (N.P.K). N-nitrogen P-phosphorus K-potassium Examples Compound D Wednesday 17 May 2023 Revision exercise (Plant nutrition) 1 .Name the 3 plant nutrients needed by plants. 2. What are the 2 groups of plant nutrients sources? 3. Give 3 examples of organic sources of plant nutrients. 4. What is a straight fertilizer? 5. Compound fertilizer supplies ……………or ………………. Nutrients. Vegetable crops • A vegetable is any part of a plant that is eaten by humans as food part of a meal. • Vegetables are grouped and named according to the part that is eaten. • These are leaf, root, fruit, flower, bulb, tuber and legume vegetables. Leaf vegetables Types of veg Legume etable cropsvegetables Fruit vegetables Root, bulb and tuber Flower vegetables Cabbage Peas Tomato Root: carrots Cauliflower Rape Green beans Pepper Parsnip broccoli Spinach Melons Beetroot Tsunga Cucumber Bulb: onion Lettuce Squash Garlic kale Egg plant Leek chillies Tuber: Irish potato Wednesday 31 May 2023 Vegetable crops 1. What is a vegetable? 2. Which one is not a vegetable from the list below? a. Covo B. cabbage C. wheat D. tomato 3. Choose a vegetable which is not a fruit vegetable. a. tomato B. pepper C. kale D. egg plant 4. From which pair of vegetables do we eat the flower? A. cauliflower and garlic B. broccoli and cauliflower C. broccoli and rape D. cauliflower and pepper 5. Give one example of a vegetable belonging to each of the following groups. a. root b. legume c. bulb 6. Name any 5 groups of vegetable classification according to the parts eaten. Growing leaf vegetables • Although there are many types of vegetables, the leaf, fruit and bulb vegetables are widely grown. • Leaf vegetables form the greater part of vegetable crops. • Leaf vegetables belong to a family called brassica. • Brassicas include cabbages, lettuce, spinach, covo and many others. • Each brassica family has got its own varieties called cultivar. • They usually grow under the same climatic conditions and are affected by the same pests and diseases. • The selection of a variety depends on the following : The intended use of the vegetable, for example, salad, stew or snacks. Days taken to mature. Disease resistant Season of the year Seedbed preparation • Brassica vegetables are usually raised in seedbeds. • The seedbeds are prepared by: • Marking the position of the bed 1 meter in width by any length using a tape measure, hammer and pegs. • Digging a seedbed to a depth of 25 to 30cm using a hoe. • Breaking lumps of soil using a garden rake. Soil requirements • Brassicas need: • Well drained soils. • Fertile soil for good growth • Slightly acidic soils (pH 5.5-6) Climatic requirements • Brassicas need cool to warm temperatures. • Very low temperatures cause cabbages to flower which is called bolting. • Brassicas can be grown throughout the year. Seedbed preparation • Brassica seedlings are usually raised in seedbeds. • A seedbed is prepared by: Marking the position of the bed 1 metre in width by any length using a tape measure, hammer and pegs. Digging a seedbed to depth of 25 to 30 cm using a hoe. Breaking lumps of soil using a garden rake. This is done in order to have a fine tilth and improve soil to seed contact. Making ridges that a 15cm high. Apply 3 to 5kg/m² of well decomposed manure. 60 to 100g/m² of compound fertilizer can be added into the soil. Management of vegetable crops • After transplanting the seedlings, the seedlings need to be looked after. (a)Controlling weeds: all vegetables must be kept weed free. • This is done either by hand pulling weeds or shallow cultivation using a hand fork. (b) Pest control: common pests that affect the brassicas are aphids and diamond black moth larva. • Aphids are small green insects that suck the juice from the leaves leaving them with curls. • They are controlled by spraying malathion using the instructions on the label. (c) Disease control: bacterial diseases are common in brassicas. • Common diseases are black rot and soft rot, especially in cabbages. • These are controlled by: Crop rotation Early planting Planting resistant cultivars (d) Top dressing: brassicas are top dressed using Ammonium Nitrate at a rate of 2.5g per plant. • Top dressing is usually done 3 or 4 weeks after germination. FIELD CROPS • Field crops are crops that are grown on a large piece of land. • Example of field crops:  Maize  Cotton  Groundnuts  Roundnuts  Wheat  Sunflower  Tobacco  Sugar cane  Tea  Coffee  Soya beans  sorghum Classification of field • Field crops can be classified according to use such crops cereal, fibre, sugar and oil. 1. Cereal crops: • A cereal is a grass grown for its edible seeds. • They are also known as grain crops. • The major cereal crops are maize, wheat, rice, barley, sorghum and millet. 2 . fiber crops : • these are crops which are grown for their fiber and are used in making textiles, ropes and rugs. • Important fiber crops are cotton, flax and sisal 3. Oil seed crops: • These crops are grown for the purpose of extracting oil from their seed. • The main oil seed crops are groundnuts, sunflower, soyabean and cotton seed. 4 . Sugar crops : • Sugar crops include sugarcane,

The following days are a jumble of gunfire, digging, gobbled food, soldiers running in and out of the forest in small groups, distant explosions, stray shells, bandaged heads and unexpected lulls. On the very first day, before dawn, I am ordered into one of the newly dug trenches. I huddle there, squeezing my magic buttons and singing songs to the dog. When the fighting stops, the dog disappears, but a new companion takes his place. A strange little soldier crawls along the trench toward me. ‘Private Sasha!’ he cries. ‘I’ve been looking for you all day long!’ He’s old, like a grandfather, a dedushka. He has a black patch over one eye, a tape measure around his neck and a row of pins threaded into his sleeve. Hanging from his belt is the most enormous pair of scissors I have ever seen and I wonder if he uses them as a weapon. He doesn’t tell me his name, so in my head he becomes Dedushka. Dedushka squats, cups his hand to his ear, peers over the top of the trench and smiles. ‘It’s safe to be upright . . . for now.’ He helps me to my feet, dusts me off and commands me to stand as tall and straight as I can. Then he measures me. Everything from head to toe – even my toes! He writes numbers in a little notebook, strings his tape measure back around his neck, salutes and hurries away. It’s all very strange, and I wonder if Dedushka has been bumped on the head during the battle and is now a little bit muddled. I should have given him a hug before he left. I chase after him but stop when I’m hit by a shovelful of flying dirt. Sleepy Bear is digging a cave! ‘Are you going to hibernate?’ I ask. Sleepy Bear chuckles. ‘No, although that would be wonderful! I could do with a lo-o-o-ong sleep.’ He sighs and closes his eyes. He doesn’t open them again and I realise that he has gone to sleep. Standing up! I shake his arm, and he opens his eyes and keeps talking. ‘No, I’m not hibernating. I’m digging a little nook where I can sleep and eat. I’ll hang up my raincape as a door that can open and close so it feels just like a real home . . . except for the lice . . . and the bad smells . . . and the bombs that make the walls shake and crumble.’ He points further along the trench to where other soldiers are digging. ‘We’re all making little houses in the ground.’ ‘Like rabbits and moles,’ I say. Sleepy Bear chuckles. ‘Yes! And soldiers who need to hide from German bullets and bombs.’ He stops digging to roll a cigarette. ‘Should I be making a house?’ I ask. ‘I want to hide from German bullets and bombs, too.’ Sleepy Bear flops to the ground, lights his cigarette, closes his eyes and takes a deep puff. I wait for him to answer, but, instead, he begins to snore! I poke him in the side. He snorts and he murmurs, ‘I think someone has already built you a house, Sasha. Keep going along this beautiful village street and you are sure to find it.’ He falls asleep once more. I kiss his dusty cheek and whisper, ‘Thank you, Sleepy Bear.’ A little way along, I see Cook in a cloud of smoke. He has lit a fire, right here in the middle of the trench, and is stirring a cauldron full of kasha. He squats as he stirs. ‘What are you doing?’ I ask. ‘Cooking supper, of course!’ he cries. ‘But why are you doing it here?’ Cook points his spoon at the ground above the trenches. ‘Because if I do it up there, my pot will be filled with holes from German bullets and all of the kasha will leak out onto the ground. It’s bad enough that our supplies can’t get through German lines and there’s nothing to cook but buckwheat for kasha. But if we lost the kasha, too . . .’ ‘Hungry soldiers,’ I say. Cook nods. ‘And grumpy!’ ‘Like Boris!’ I gasp. ‘Even worse,’ warns Cook. I picture the kasha pot full of bullet holes. And then I realise that if the kasha pot were full of holes, then Cook would be, too. I wrap my arms around Cook’s neck and say, ‘I think this is a very good place for cooking our supper.’ I kiss his smoky cheek and run along. At the end of the trench, I find the biggest hole of all. It’s wide and deep and as busy as a beehive in a blossom tree. Above, a group of soldiers is rolling logs into place for a roof, while below, typewriters rattle and pencils scratch and papers flutter and voices crackle out of five different radios. Their words tangle together to tell a strange wartime fairy tale about German guns and a loving father called Stalin and a Red Army regiment that is lost in the deep, dark forest and a wicked beast called Hitler and a delivery of vegetables that was hit by a bomb and blown into a million tiny pieces too small even to make soup. In the middle of it all, wrestling with a rumpled map, his rifle still slung over his shoulder, is Major Scruff. ‘Major Scruff!’ I run and jump into his arms. ‘Is this our new home?’ ‘Yes, Sasha. I suppose it is.’ ‘Is it safe from German bullets and bombs?’ I ask. He stares at me. ‘Were you scared in the trenches today, Sasha?’ ‘No,’ I reply. ‘I had magic buttons and a dog and some songs to sing. Were you scared in the forest, Major Scruff?’ ‘Yes,’ he says. ‘Poor Major Scruff!’ I press my hand against his cheek. The dark, rough stubble is grubby with grit and his eyelids are taking a long time to open after every blink. ‘You need a shave and a nap!’ I scold. He chuckles. ‘I am too tired to shave and too busy to nap.’ I scrunch my nose while I consider his problem. ‘I know!’ I cry. ‘You nap and I will shave your whiskers. That will be two jobs tumbled into one!’ And so that’s what we do. Major Scruff slumps into a chair and snoozes while I lather his face with soapy water and shave his whiskers. The soap suds travel from his face, up into his hair and down the front of his uniform, and I have to shave his jaw and chin three times because I keep missing bits, but I finally get it all done. I am just wiping his cheeks dry when the dog appears. He licks my hand, then stretches up and licks soap suds from Major Scruff’s ear. Major Scruff wakes with a start. He feels his newly shaved face and cries, ‘Wonderful, Sasha! I feel smooth, clean, rested and ready for action.’ He ruffles my hair. ‘We must do this again tomorrow. Although next time, you might wake me with a gentle shake of the shoulder instead of licking my ear.’

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

Ordered Pair Quadrant Sort

Orded pair

4.5.1 Order Pair Recognition

Volume of prism,orderd pairs and measure of center

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