1. Given the set A = {1, 2, 2, 4, 5, 6}, derive the power set of A.

2. Given sets A = {1, 2}, B = {x, y, z}, C = {p, q}, derive the Cartesian product A B C.

3. Determine whether the following expression is true. P(A B) = P(A) P(B)

4. (a) Write the set expression for all even integer numbers greater than 26 and less than 50. (b) Determine the cardinality of the set

5. Let A = {1, 2, 3, 4, 5, 6}. Find all sets B P(A) that have the property {2, 3, 5} B.

6. Draw the Venn diagram for following set expression: (A B) \ C

7. Let A2 be the set of all multiples of 2 except for 2. Let A3 be the set of all multiples of 3 except for 3. And so on, so that An is the set of all multiples of n except for n, for any n 2. Describe (in words) the set A2 A3 A4 Hint: It might help to think about what the union A2 A3 is first. Then think about what numbers are not in that union. What will happen when you also include A5 ?

8. The following functions all have domain {1, 2, 3, 4, 5} and codomain {1, 2, 3}. For each, determine whether it is (only) injective, (only) surjective, bijective, or neither injective or surjective. (a) f = 1 2 3 4 5 1 2 1 2 1 (b) f = 1 2 3 4 5 1 2 3 1 2 (c) f(x) = x, ifx 3 x 3, ifx > 3

9. Suppose f: N 7 N satisfies the recurrence f(n + 1) = f(n) + 3. For each of the initial conditions below, find the value of f(5). (a) f(0) = 0 (b) f(0) = 1 (c) f(0) = 2 (d) f(0) = 100