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For all sets A, B and C

Is (A ∩ B) ∪ C = A ∩ (B ∪ C)? Justify your statement.

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No. consider the following sets A, B and C :

A = {1, 2, 3}

B = {2, 3, 5}

C = {4, 5, 6}

Now

(A ∩ B) ∪ C = ({1, 2, 3} ∩ {2, 3, 5}) ∪ {4, 5, 6}

= {2, 3} ∪ {4, 5, 6}

= {2, 3, 4, 5, 6}

And

A ∩ (B ∪ C) = {1, 2, 3} ∩ [{2, 3, 5} ∪ {4, 5, 6}

= {1, 2, 3} ∩ {2, 3, 4, 5, 6}

= {2, 3}

Therefore, (A ∩ B) ∪ C ≠ A ∩ (B ∪ C)

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