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

2916 239 WBJEEWBJEE 2009Sets Report Error

A

$B$

20%

B

$A - B$

22%

C

$A \cap B$

47%

D

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

11%

Solution:

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