If A and B are two sets, then A ∩ (A ∪ B)' is equal to ____________.

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Solution

For sets A and B
A ∩ (A ⋃ B)'
= A ⋂ (A' ∩ B')
= (A ∩ A') ∩ B' (using associative properly of sets)
= ϕ ∩ B'
Hence, A ∩ (A ⋃ B)' = ϕ

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