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Consider the following assertions: Assertion 1: If A ∪ B = A ∪ C and A ∩ B = A ∩ C, then B = C. Assertion 2: A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C). Choose the correct statement about these assertions.

1. Assertion 1 is true and Assertion 2 is true; Assertion 2 correctly explains Assertion 1.
2. Assertion 1 is true and Assertion 2 is true; Assertion 2 does not correctly explain Assertion 1.
3. Assertion 1 is false and Assertion 2 is true.
4. Assertion 1 is true and Assertion 2 is false.

Correct answer: Assertion 1 is true and Assertion 2 is true; Assertion 2 does not correctly explain Assertion 1.

Solution

Assertion 1 is a valid theorem: if A∪B=A∪C and A∩B=A∩C then B=C. Assertion 2 is the distributive law A∪(B∩C)=(A∪B)∩(A∪C), also true. Both are true, but the distributive law does not directly explain the cancellation result, so 'both true, A2 does not explain A1' is correct.

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