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If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C, then
- A = C
- B = C
- A ∩ B = ∅
- A = B
Correct answer: B = C
Solution
The conditions A ∩ B = A ∩ C and A ∪ B = A ∪ C imply that the elements of B and C must be identical when considering their relationship with A. Since both intersections and unions yield the same results, it follows that B and C must contain the same elements, leading to the conclusion that B = C.
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