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By Alan Doerr, Kenneth Levasseur
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The instructor told the truth. ) Case III: Your final exam score was greater than 95, but you did not receive an A. The instructor lied. Case IV: Your final exam score was greater than 95, and you received an A. The instructor told the truth. To sum up, the only case in which a conditional proposition is false is when the condition is true and the conclusion is false. The order of the condition and conclusion in a conditional proposition is important. If the condition and conclusion are exchanged, a different proposition is produced.
E, 3)}. Since the first entry of each pair can be any one of the five elements a, b, c, d, and e, and since the second can be any one of the three numbers 1, 2, and 3, it is quite clear there are 5 · 3 = 15 different elements in A ⇥ B. 4 (A True-False Questionnaire). A person is to complete a truefalse questionnaire consisting of ten questions. How many different ways are there to answer the questionnaire? Since each question can be answered either of two ways (true or false), and there are a total of ten questions, there are 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 = 210 = 1024 different ways of answering the questionnaire.
How many seating arrangements of these persons can there be (a) If you are a total stranger? (b) If you are A and B’s mother? This problem is designed to show you that different people can have different correct answers to the same problem. 14. How many ways can a student do a ten-question true-false exam if he or she can choose not to answer any number of questions? 15. Suppose you have a choice of fish, lamb, or beef for a main course, a choice of peas or carrots for a vegetable, and a choice of pie, cake, or ice cream for dessert.