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The second associative law states that if A, B, and C are sets, then A(B C) = (A B) C. We prove this statement by

The second associative law states that if A, B, and C are sets, then A(B C) = (A B) C. We prove this statement by proving the below two assertions.

(a) Prove that A (B C) (A B) C . Hint: To prove this, start with an element x A (B C) and show that x (A B) C.

(b) Prove that (A B) C A (B C).

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