1. Let A = {a, c, e, h, k}, B = {a, b, d, e, h, i, k, l}, and C = {a, c, e, i, m}. Find each of the following sets.

(a) A B

(b) A B C

(c) A C

(d) A B C

(e) A B

(f) A (B C)

2. Prove or disprove that if A, B, and C are sets then A (B C) = (A B) (A C).

3. Let f(n) = 2n + 1. Is f a one-to-one function from the set of integers to the set of integers? Is f an onto function from the set of integers to the set of integers? Explain the reasons behind your answers.

4. Suppose that f is the function from the set {a, b, c, d} to itself with f(a) = d, f(b) = a, f(c) = b, f(d) = c. Find the inverse of f.