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MATHEMATICS EXAM CTL Revision v0.8 ES CW 1 Clear Thinking and Logic Revision Questions for Major Test Question 1 Consider each of the sentences below and say whether it functions as a statement (asserts something to be a fact, and is therefore capable of being true or false); an imperative (either commands or requests or suggests that a particular action be performed); an interrogative (requests information as a question); rhetorical question (looks like a question but is not a request for information but states information or makes a point) ; or a performative (the writing or speaking of the sentence is itself an action of a certain kind). 1. All cats are felines. _________________________________________________________________________ 2. Place the ingredients in a mixing bowl. __________________________________________________________________________ 3. I now pronounce you King of England. ___________________________________________________________________________ 4. What day is it today? ___________________________________________________________________________ 5. What kind of fool do you think I am? _____________________________________________________________________________ (5 marks) Question 2 For each of the following statements say whether it is true or false. 1. A deductive argument is one that is valid. 2. Valid arguments with true premises also have true conclusions. 3. Sentences can be true, false, or neither. CTL Revision v0.8 ES CW 2 4. Arguments can be either true or false. 5. Both deductively sound and inductively sound arguments must have all true premises. (5 marks) Question 3 Arguments are made up of a series of statements, one of which is intended to be true (the conclusion) based on the truth of the others (the premises). Not all series of statements or passages are arguments. Explanations, are not intended to provide evidence to convince a doubter that something is a fact, they are used in circumstances where it is taken for granted that everybody knows that something is a fact, in order to explain why it is a fact, or what caused it to be a fact. Reports are intended to provide information about a topic, situation or event, information which it is hoped that the audience will believe, but where it is not the case that one statement is supposed to be shown to be true on the basis of other statements; illustrations are attempts to make a statement clearer or easier to understand by providing example(s) which illustrate the original statement; mere assertions are controversial claims not supported by reasons; conditional statements are statements of the form If…then…. For each of the following passages say whether it is an argument, an explanation, a report, a mere assertion, a conditional statement, or an illustration. If the passage contains an argument state the conclusion and identify any inference indicators. Say whether the inference indicators are premise or conclusion indicators. If the passage contains an explanation state the explanandum (i.e. the fact for which an explanation is being offered). 1. The last world war occurred more than seventy years ago, and there was never any serious fighting on Australian soil. Consequently, it is highly likely that people in Australia today do not understand the horror of a world war. 2. Australia has many unique natural features and sites that every tourist should see. For example, the Great Barrier Reef, Uluru (also known as Ayers Rock), the opals in Coober Pedy, and the scenery on Kangaroo Island. CTL Revision v0.8 ES CW 3 3. All people who like rap music are either dumb or under the age of fifteen. 4. The two escaped prisoners scaled a wall, stole a car, and then headed for the state border. The police tried valiantly to catch them, but the stolen car was a Lamborghini and could go faster than both the police cars and the police helicopters. The prisoners remain on the run. 5. Smoking cigarettes is very bad for you because the smoke you inhale contains many highly carcinogenic substances. 6. If play is not disrupted by rain then India will win the test match against Australia. ______________________________________________________________________________________ ______________________________________________________________________________________ (9 marks) Question 4 Deductive arguments are good only if they are valid. The method of logical analogy can be used to show that an argument is invalid, and involves producing an argument of the same form as the original argument with obviously true premises and an obviously false conclusion. Apply the method of analogy to the arguments below as follows: (i) Write down the general logical form of the argument using A, B, and C. (ii) Produce an argument of your own which is of that form and has obviously true premises and an obviously false conclusion. 1. All sheep are woolly. No fish are sheep. So, no fish are woolly. (4 marks) CTL Revision v0.8 ES CW 4 Question 5 Deductive arguments are good only if they are valid. The method of counterexample can be used to show that an argument is not valid and involves describing a “hypothetical scenario” in which the premises of the original argument are obviously true and the conclusion obviously false. Apply the method of counterexample to the following invalid argument. Begin your answer with the phrase “Suppose that the premises are true [Clearly state and number each premise], but suppose also that…” and then go on to describe a hypothetical scenario in which the premises of the argument would be true and the conclusion would be false. 1. Sarah had a lot of money. She got advice on how to invest it from her financial advisor. Now Sarah has no money. Her financial advisor must be a thief. (5 marks) Question 6 State whether the following arguments are valid, strongly reliable or neither. 1. 95% of Swiss people can speak German. Roger Federer is a Swiss person. So, Roger Federer can speak German. ________________________________________________________________________________ 2. Winston Churchill hates Hitler. Joseph Stalin hates Hitler. So, Winston Churchill loves Joseph Stalin. _________________________________________________________________________________ (2 marks) CTL Revision v0.8 ES CW 5 Question 7 Suppose that it is true that Some students are racing car drivers and represent this information in a Venn diagram. Then represent each of the following statements in a Venn diagram and judge, on the basis of those diagrams, whether the statements are true, false, or could be either (given the original claim above i.e. that it is true that Some students are racing car drivers). 1. All students are racing car drivers. 3. Some non-students are non-racing car drivers. 3. All non-students are non-racing car drivers. (7 marks) CTL Revision v0.8 ES CW 6 Question 8 Represent the following categorical syllogisms in the form of a Venn diagram. On the basis of the Venn diagram state whether the argument is valid or invalid and briefly justify your answer by reference to relevant features of the Venn diagram. 1. Some scientist is a male. All philosophers are males. So, some scientist is a philosopher. 2. No fish is able to live on land. All people can live on land. So, no person is a fish. (10 marks) Question 9 Translate each of the following statements into standard categorical form. 1. Only saints are morally perfect. ______________________________________________________________________________________ 2. New York is a large city. ______________________________________________________________________________________ (2 marks) CTL Revision v0.8 ES CW 7 Question 10 Using ‘P’, ‘Q’, ‘R’ etc, write down the form of each of the following arguments. Also, state the name of the argument form, and finally say whether the argument is valid or invalid 1. If you buy today, I will give you a 10% discount. You are buying today, so I will reduce the price by 10%. (5 marks) Question 11 Each of the following passages contains an argument. Represent the argument’s structure in a diagram following these steps: Look for inference indicators. Mark each inference indicator by putting <…> around it. Identify and mark off /…/ each statement, numbering each in the order in which it appears in the text. If the argument is complex, identify the sub-conclusion(s) and the main conclusion. Underline the main conclusion. Where more than one reason is put forward in support of the same conclusion judge whether the reasons support the conclusion jointly or independently. Construct a diagram. 1. All university students should study critical thinking. After all, critical thinking is necessary for surviving in the new economy because in many new jobs there is a very large amount of information that we need to be able to critically evaluate. Also, critical thinking can help us reflect on our values and purposes in life. Finally, critical thinking helps us improve our study skills. (7 marks) CTL Revision v0.8 ES CW 8 2. If it rains, there will be no picnic today. It is raining, so there will be no picnic today. Also, no one was told that there was going to be a picnic anyway, and the council have decided that they are not going to let anyone use the park for a picnic for the rest of the month. (7 marks) 3. No one is going to come to my birthday party! Sarah won’t come because she has study to do. Jim won’t come because he already said that he will be going to the movies with some other friends. On top of all of those things, I forgot to invite any other people. (9 marks) (Total marks for Question 11 – 23 marks) 4th Floor Copier-20190726151316 55BW-5e-20120610101554