浙江大学翁燕玲离散数学及其应用偶数题答案.pdfVIP

Sample Solutions on HW1 (29 questions in total) Sec. 1.1 2, 6(d, e), 14( e), 22, 28(b), 32(f), 48 2. a) This is not a proposition; it’s a command. b) This is not a proposition; it’s a question. c) This is a proposition that is false. (This is not a common knowledge to our students, so a full credit will be given as long as a proposition is been determined.) d) This is not a proposition; its truth value depends on the value of x. e) This is a proposition that is false. f) This is not a proposition; its truth value depends on the value of n. 6. d) False, because the hypothesis of this conditional statement is true and the conclusion is false. e) False, because the first part of this biconditional statement is false and the second part is true. 14(e) (p  q)  r 22 a) If you get promoted, then you wash the boss ’s car. b) If the winds are from the south, then there will be a spring thaw. c) If you bought the computer less than a year ago, then the warranty is good. d) If Willy cheats, then he gets caught. e) If you can access the website, then you must pay a subscription fee. f) If you know the right people, then you will be elected. g) If Carol is on a boat, then she gets seasick. 28(b) Converse: Whenever I go to the beach, it is a sunny summer day. Contrapositive: Whenever I do not go to the beach, it is not a sunny summer day. Inverse: Whenever it is not a sunny day, I do not go to the beach. 32(f) p q ¬q p  q p  ¬q (p  q) (p  ¬q) T T F T F T T F T F T T F T F F T T F F T T F T 48 This cannot be a proposition, because it cannot have a truth value. Indeed, if it were true, then it would be truly asserting that i