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

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

WBJEEWBJEE 2009Sets

Solution:

Now, $A-\left(A-B\right)=A-\left(A \cap B^{c}\right)$
$=A \cap\left(A\cap B^{c}\right)^{c}$
$=A\cap\left(A^{c}\cup B\right)$
$=\left(A\cap A^{c}\right)\cup\left(A \cap B\right)$
$=A\cap B$