Practice Problems
Answers
(b) If an object does not have 3 sides, then it is not a triangle. True.
9. (a) If your car does not get at least 24 miles per gallon, then it is not tuned properly.
(b) If you can not have dessert, then you did not eat your vegetables.
11. (a) If you will not vote for me, then you do not love your country.
(b) If not only outlaws have guns, then guns are not outlawed. (poor English If someone legally has a gun, then guns are not illegal.
13. (a) Both and are not positive.
(c) 8 is not a prime number.
15. (a) For some numbers and .
(b) Some snake is not poisonous.
(c) Some dog can climb trees.
17. If is an integer, then is an even integer. True.
Converse: If is an even integer, then is an integer. True.
(It is not likely that
these were the statements you thought of. There are lots of other examples).
19. (a) False. Put and . Then , but .
(b) False. Put and . Then , but .
(c) True.
21. (a) True.
(b) False. Put and . Then is not a linear function.
(c) True.
23. (a) If and are prime numbers, then is prime. False: take and .
(b) If and are prime numbers, then is not prime. False: take and .
(c) If is a prime number, then is odd. False: take . (this is the only counterexample)
(d) If is a prime number, then is even. False: take (or 5 or 7 or ...)
25. (a) If is a solution of , then is odd. False: take .
(b) If a 3–sided polygon has equal sides, then it is a triangle. True. (We also have nonequilateral triangles .)
(c) If a person is a calculus student, then that person studies hard. False (unfortunately), but we won't mention names.
(d) If is a (real number) solution of , then is even. False: take .