If A and B are two sets satisfying A - B = B - A, then which one of the following is correct?a)A =φb)A ∩ B = φc)A = Bd)None of theseCorrect answer is option 'C'. Can you explain this answer?

Question

If A and B are two sets satisfying A - B = B - A, then which one of the following is correct?a)A =&phi;b)A &cap; B = &phi;c)A = Bd)None of theseCorrect answer is option 'C'. Can you explain this answer?

Answer

B

b) A ⊆ B

c) B ⊆ A

d) A = B

To determine the correct answer, let's analyze the given equation A - B = B - A.

The set difference A - B represents the elements that are in A but not in B. Similarly, B - A represents the elements that are in B but not in A.

If A - B = B - A, it implies that the elements that are in A but not in B are equal to the elements that are in B but not in A. This can only be true if both A and B have the same elements, i.e., A = B.

Therefore, the correct answer is:

d) A = B

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