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If A and B are non-empty sets with A containing B, then which of the following is true?

1. B' − A' = A − B
2. B' − A' = B − A
3. A' − B' = A − B
4. A' ∩ B' = B − A

Correct answer: B' − A' = A − B

Solution

With B contained in A: B' - A' = B' intersect A = A intersect B' = A - B. Since B is a subset of A, B - A is empty, so option 'B'-A' = B-A' is false. The correct identity is B' - A' = A - B.

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