Question

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

• A. $B$
• B. $A-B$
• C. $A \cap B$
• D. $A^{c} \cap B^{c}$

Answer 1

Answer: (C)

$A \cap B$

Answer 2

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