For any two sets A and B, prove that (A )-B = A- B - Vidyadip

Question

For any two sets A and B, prove that $(\text{A}\cap\text{B})-\text{B = A}- \text{B}$

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Answer

$\text{(A} \cup\text{B) – B = (A} - \text{B)}\cup\text{(A} - \text{B)}$ $= \oint\cap \text{ (A} - \text{B)}$ $= \text{A} - \text{B}.$

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