Answers for the even problems in Gemign. Sections 2.1-3

Answers for the odd problems are in the back of the text.

Note that these are just answers, not explanations - ask during the class review, or at an extended office hour.

2.1#2: (a) If I will go then you will say so. (b) If I think about study, then I want to play.. (c) If you look for it then you will find it. (d) If someone is an elephant then he is not a man. (e) If the angles of a triangle is congruent to those of another, then they are similar. (g) If you live then you eat. (h) If someone is ambitious then they work hard.

2.2#2: (a) It is not mild out today. (b) Some of my cows are not in the pasture. (c) All of my cows are not in the pasture. (d) More than one of my cows is in the pasture. (e) There exists a pair of men who are alike. (f) No one else cares, but I do care. (g) It sometimes rains and I do not wear my coat.

2.3#2: (a) x=1 is one counterexample; another is 0. (b) See below

(c) 1^2+1^2+1^2+2^2 is odd, not even. (d) Penguin (e) See below

2.3#4: No; to prove that "Some men are silly" is false you'd have to show somehow that all men are not silly. You can, however, prove that "All men are silly" is false with a counterexample, by trotting out one non-silly man.

Picture for 2.3b,e: