Question: Prove that A (A B) = A for any sets A and B. (This is the absorption law for sets.) Use the mutual containment method,

Prove that A (A B) = A for any sets A and B. (This is the absorption law for sets.) Use the mutual containment method, i.e., prove that the set on the left-hand side is a subset of the set on the right-hand side and vice versa. Write your proof for each part in stepwise fashion and provide justification for each step.

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