Problem 1: [30 pts] (Sets) Directions: Recall that if A and B are sets, we have the following definitions. . We say A is a subset of B, and write A C B if for every a E A, we also have a E B. . We say A = B if for every a E A and be B, we have a E B and be A. Prove the statements below. Use the next page if you need more space. A. [10 pts] Use the definitions above to show that A = Biff A C B and B C A. B. [10 pts] Prove that SC Tiff SUT = T. C. [10 pts] If A C C and B C C, prove the DeMorgan Law (A UB) = An Be