1.5 Homework Partial Solutions
#8 : If m and n are both odd, then m = 2K + 1 and n = 2L + 1 for some K, L integers.
Therefore m + n = 2K + 1 + 2L + 1 = 2L + 2L + 2 = 2(K + L + 1), so m + n is even since
it is 2 times an integer.
#11 : If m is odd and n is
1.2 and 1.3 Homework Partial Solutions
Section 1.2
#3 : If Fernando buys a computer, then he obtained $2000.
#6 : If the chairperson gives a lecture, then the audience will go to sleep.
#14 : (p q ) r is false since p q is true and r is false. (TRUE FALSE
1.3 and 1.4 Homework Partial Solutions
Section 1.3
#20 : There is someone who if she is a professional athlete, then she plays soccer. (TRUE)
#23 : Everyone plays soccer or is a professional athlete. (FALSE)
#29 : (P (x) Q(x)
#38 : TRUE since when x = 3,
Review Answers
1. Show, by giving a proof by contradiction, that if four teams play seven games, some pair of
teams plays at least two times.
Proof: Suppose the teams are A, B, C, D. We assume p and q. In this case, q is no pair
of teams plays two times,
3.2 Homework Partial Solutions
#2 : Not transitive since (1, 3), (3, 4) R, but (1, 4) R. Thus, it is not an equivalence
relation.
#3 : This is an equivalence relation. The equivalence classes are [1] = cfw_1, [2] = cfw_2, [3] =
cfw_3, [4] = cfw_4.
#5 : Th
1.1 Homework Partial Solutions
#2 : This is a question, not a statement, i.e., not a proposition.
#6 : This is a proposition, and its negation is:
The line Play it again, Sam does not occur in the movie Casablanca.
#10 : The negation of the statement is: