Prove that (AAB) AA = B for all sets A and B. - * Prove or...

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Prove that (AAB) AA = B for all sets A and B. - * Prove or disprove: If A, B, and C are sets satisfying AAC = BAC, then A= B. Prove or disprove: AA(BUC) = (AAB) U (AAC) for all sets A, B, and C. Prove or disprove: AA(BOC) = (AAB) n (AAC) for all sets A, B, and C. Prove or disprove: AU (BAC) = (AUB)A(AUC) for all sets A, B, and C. Prove or disprove: An (BAC) = (An B)A(ANC) for all sets A, B, and C. Is A commutative? If so, prove it; otherwise, give a counterexample. Prove that (AAB) AA = B for all sets A and B. - * Prove or disprove: If A, B, and C are sets satisfying AAC = BAC, then A= B. Prove or disprove: AA(BUC) = (AAB) U (AAC) for all sets A, B, and C. Prove or disprove: AA(BOC) = (AAB) n (AAC) for all sets A, B, and C. Prove or disprove: AU (BAC) = (AUB)A(AUC) for all sets A, B, and C. Prove or disprove: An (BAC) = (An B)A(ANC) for all sets A, B, and C. Is A commutative? If so, prove it; otherwise, give a counterexample.

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1 Prove AAB AA B for all sets A and B Proof Let A and B be two arbitrary sets We want to prove that AAB AA B To do this we will use the Laws of Set Theory First let us consider the left side of the eq... View the full answer