[Proof Methods and Strategies]

1) Use a proof by cases to show if x is an integer then x2 + x is even.

2) Give a direct proof that the sum of two odd numbers is even.

3) Give a proof by contraposition that if x2 is odd, x is odd.

4) Give a proof by contradiction that if n+2 is even then n is even.

5) Without using Disjunctive Syllogism, prove that p U q and p imply q

[Sets]

6) SupposethatA={2,3,4,7},B={3,7},C={2,4,7},andD={3,5,7}.Determine which of these sets are subsets of which other of these sets.

7) What is the cardinality of each of these sets?

a)

b) {0}

c) {}

d) {{, {}}}

8) LetA={1,2},B={x,3,z},andC={2,y}.Find a) ABC

b) CBC

9) Find the truth set of each of these predicates where the domain is the set of integers.

a) Q(x): x

b) R(x): log(x) [Note: For this course, log is base 2 unless stated otherwise.]

10) Let A = {a,b,c,d,e} and B = {a,b,c,f}. Find:

a) AB b) AB c) AB d) BA

11) For any sets A,B,and C,prove that if A B A C and A not equal ,then B C.