[Proof Methods and Strategies]

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

[Sets]

2) Suppose that A = {2, 3, 4, 7}, B = {3, 7}, C = {2, 4, 7}, and D = {3, 5, 7}. Determine which of these sets are subsets of which other of these sets.

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

a)

b) {0}

c) {}

d) {{, {}}}

4)Let A = {1, 2}, B = {x, 3, z}, and C = {2, y}.

Find a) A B C

b) C B C

5)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.]

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

a) A B

b) A B

c) A B

d) B A

6)For any sets A, B, and C, prove that if A B A C and A , then B C.