Assume A, B, and C are all sets that lie in a common universal set. Can you conclude that A = B given the following statements? If so, prove your answer using only set identities, as seen in Lecture and in ZyBooks 4.4. If not, provide a single counterexample. Hint 1: Usually in proof using set identities, you must start from one side of the identity and try to reach to the other side of the identity. It means that, you should start your proof by: A = ... Hint 2: Usually in proof using set identities, you should be able to involve the given hypotheses into your proof. Consider using Absorption law or Identity law to involve the hypotheses into your proof. Examples: P = P (P Q) because of Absorption law or P = P U because of Identity law. Hint 3: For more help, look at Problem 4 in Discussion 4 (given solution by method 2).

a) A C = B C

b) A C = B C

c) A C = B C and A C = B C