2 Set Operations 2.1 6 points Suppose A, B, and C are sets. 2.1.1 Suppose also that AUC = BUC. Can we conclude that A - B? Prove your answer, and clearly state what type of proof you are using 2.1.2 Suppose also that AnC=Bnc. Can we conclude that A = B? Prove your answer, and clearly state what type of proof you are using 2.1.3 Suppose also that AUC - BUC and ANC-BAC. Can we conclude that A - B? Prove your answer, and clearly state what type of proof you are using 2.2 6 points The symmetric difference of two sets AB is the set of elements that are in either the set A, or in the set B, but not in both. Now suppose A, B, and C are sets. Does A (BC) -( AB) C? Explain why or why not in a few sentences (you do not need to give a formal proof). 2.3 6 points Suppose A, B, and Care sets. Explain why AU BUC| - |A1+1B1+IC-IAN BL-1AC-BOCI+ABC Explain in a few sentences (you do not need to give a formal proof)