For any two sets A and B, A ? (A ? B) equals

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Solution

Q.
For any two sets $A$ and $B$ , $A - (A - B)$ equals

1 $B$

2 $A - B$

3 $A \cap B$

4 $A^{c} \cap B^{c}$

Ans.
(3)

$A - (A - B) = A \cap {(A \cap B^{c})}^{c} = A \cap (A^{c} \cup B)$

$= ϕ \cup (A \cap B) = A \cap B$

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