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Question
For all sets A, B and C is (A ∩ B) ∪ C = A ∩ (B ∪ C)? Justify your statement.
Solution
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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