Question: Prove Theorem 1.4.11. In theorem For every two sets A and B, A B and A Bc are disjoint and A = (A

Prove Theorem 1.4.11.
In theorem
For every two sets A and B, A ∩ B and A ∩ Bc are disjoint and
A = (A ∩ B) ∪ (A ∩ Bc).
In addition, B and A ∩ Bc are disjoint, and
A ∪ B = B ∪ (A ∩ Bc).

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