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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 false and Assertion 2 is true.

Solution

Assertion 1 is false because the conditions given do not guarantee that sets B and C are equal; they can still differ while having the same unions and intersections with A. Assertion 2 is true as it correctly represents the distributive property of set operations, showing that the union of A with the intersection of B and C is equivalent to the intersection of the unions.

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