"Truth conditions" are the conditions in the world that...

are the same for every proposition

A contradiction is a proposition whose...

truth conditions are always fulfilled

A tautological expression inside a sentence is an expression that...

contains one or several redundant words

is always a true part of the predicate

"My opinion is exactly what I think" What is this?

A synthetic proposition with a tautological expression

"We'll arrive when we arrive" What is this?

A synthetic proposition with a tautological expression

"We took a rest at the summit at the top of the mountain" What is this?

A synthetic proposition with a tautological expression inside

"She found an organized chaos in his room" What is this?

A synthetic proposition with an oxymoron inside

In a pure semantic perspective, tautologies and contradictions...

don't add any information to a conversation

play an important in our conversations

Propositions and truth

General Mathematics covers the real number system, functions and their graphs (linear, quadratic, polynomial, exponential, and logarithmic), sequences and series, simple and compound interest, annuities and other financial mathematics applications, logic and reasoning (including propositions, truth tables, and arguments), and basic business mathematics involving problem solving and decision making.

Match the word to its synonym level B1 CEFR. Use the vocabulary exactly adverb precisely except that aside from exist verb to be real existing adjective real, current Example: Flying cars are not practical with existing technology. existence noun reality Example: The existence of black holes has been confirmed by indirect observation. extraordinary adjective unusual feature noun important part of something Example: The Ramon Crater is a unique feature of the Negev Desert. feedback noun reaction figure noun shape Example: I can’t tell if that figure in the shadows is a man or a woman. figure out verb understand Example: I just can’t figure out how the magician did that amazing trick. financial adjective related to money Example: Her family is having financial problems so they can’t travel overseas this year. finance verb pay for Example: If I can’t get a loan from the bank, I won’t be able to finance a new apartment. finance noun money Example: An expert in finance predicts a global recession. finding/findings noun discoveries; results of a study Example: According to the findings of the police investigation, this is the gun which fired the fatal bullet. flexibility noun willingness to change flexible adjective adjusts easily Example: I’d prefer to meet on Monday morning but I can be flexible depending upon your schedule. flood noun a lot of water flood verb to cover with too much water flu noun type of sickness focus on/upon verb pay attention to Example: You should focus on your schoolwork if you want to improve your grades. focus noun attention People with attention deficit disorder lose focus easily. frequency noun how often frequent adjective very often Example: Hanah is a frequent customer and everyone at the store knows her. fresh adjective new Example: We need some fresh ideas if we’re going to solve this problem. frighten verb scare from preposition position, starting point gain verb make an increase, profit, earn Example: I have nothing to gain by choosing sides so I shall remain neutral. gain noun profit, amount earned generate verb create, make Example: Chat GPT can generate text written in any style you choose. guidance noun help, advice hopeful adjective optimistic, having a positive outlook Example: The farmers are hopeful that we will have rain this winter. hopefully adjective with luck ideal adjective best, most preferable Example: Nuclear power may not be an ideal solution to global warming, but it’s certainly worth considering. illness noun sickness, disease illustrate verb draw pictures illustration noun picture, image Example: Children’s storybooks have colorful illustrations. image noun picture, especially on film or television Example: The mother of the pop singer cried when she first saw her daughter’s image on television. in preposition within, inside, into in terms of regarding Example: That company makes a great product but they’re lacking in terms of customer service. in actual fact in truth Example: The mayor says the city is a safe place to live, but in actual fact the violent crime rate is very high. in connection with about Example: Police arrested four men in connection with the robbery. in that case if that is true Example: Billy Bob: “Traffic could be heavy tomorrow.” Peggy Sue: “In that case, we better leave early.” in the meantime while, during Example: The new computers won’t arrive until next week, but we can keep using the old ones in the meantime. initial adjective first Example: Her initial reaction to that song was negative, but over time she’s come to like it. initially adverb at first instruction noun teaching, order Example: Most new electronic devices come with a set of instructions. intelligence noun smartness Example: Since you have a degree from a good university, I assume you have sufficient intelligence to understand this problem. intelligent adjective smart Example: Joe isn’t very intelligent, but he is a kind person with a warm heart. interest noun attraction Example: Yossi has little interest in politics, whereas his wife goes to all the protests and demonstrations. interest verb to attract Example: Sports don’t really interest me, but my brother is a big basketball fan. introduce verb to show something new Example: Today in class I will introduce the basic concepts of literary analysis. invest verb to put money into something in order to earn money Example: Joe invested in cryptocurrency and lost a lot of money. investor noun one who puts money into something in order to earn money Example: Venture capitalists are investors who put money into risky start-up businesses. investment noun putting money into something in order to earn money Example: Buying real estate in Israel is a very safe investment because the value never goes down. investigate verb research, study Example: The police collected evidence to investigate the murder. investigation noun study Example: The police don’t have a suspect for the murder as the investigation isn’t finished yet. investigator noun detective Example: Detective Schmendrick is the lead investigator for the murder case. just about almost Example: I’m just about done here so I’ll be there shortly. keep on doing verb continue Example: You’re crazy if you keep on doing the same thing and expect different results. kind of type of Example: What kind of dog is that, a poodle? knowledge noun awareness Example: John failed the test due to lack of knowledge of the material. lack verb not having, missing Example: John failed the test due to lack of knowledge of the material. landscape noun the view of the land likely adjective, adverb probably Example: When we learn from our mistakes, we’re not likely to forget. limited adjective restricted Example: We should go to the store today because the sale is for a limited time only. limitation noun restriction little adjective small, not a lot Example: She always tells the truth. I have little reason to doubt her. look at verb see Example: People used to read newspapers on the train. Nowadays they just look at their phones. low adverb to a small amount or level Example: I have to charge my phone because the battery is running low. material noun documents, information Example: We have a lot of material to cover before the end of the semester. meaning noun significance mean verb to have significance or purpose means noun form of, by the use of Example: They communicate by means of radio. measure noun step Example: The teacher took measures to prevent cheating during the test mention verb to say, point out Example: The coach said the team played very well today but didn’t mention any player specifically. miss verb (1) fail to catch (2) wishing to see somebody Examples: (1) The football player kicked the ball but missed the goal. (2) Wow, it’s good to see you! I’ve missed you so much! misunderstand verb understand incorrectly Example: I’m afraid I misunderstood the instructions. Could you repeat them please? more or less approximately, somewhat, to a varying degree Example: This is more or less a religious neighborhood, though there are a few secular families. must modal verb have to naturally adverb as expected, normally nature noun (1) open air (2) character Examples: (1) We like to go hiking in nature reserves. (2) Pit bulls are aggressive by nature.

Propositions and Symbols

Prepositions and Adverbs

Prepositions and word building

Prepositions and conjunctions

Prepositions and prepositional phrases 2

Prepositions and prepositional phrases +

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