Choose the true statement representing union distributing over intersection.
A∪(B∩C)=(A∪B)∩(A∪C)
The distributive law of union over intersection states that for any sets A, B and C, the union of A with (B ∩ C) equals the intersection of (A ∪ B) and (A ∪ C).
Check: an element lies in A ∪ (B ∩ C) if it is in A, or in both B and C. In either case it lies in A ∪ B and also in A ∪ C, and the reverse also holds.
The form A ∪ (B ∩ C) = (A ∩ B) ∪ (A ∩ C) is not a valid law, and A ∩ (B ∪ C) = (A ∪ B) ∩ (A ∩ C) is also invalid; the correct intersection-over-union law is A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C).
Hence, the answer is A∪(B∩C)=(A∪B)∩(A∪C).
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