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

The correct option is C

$A\cap B$

Explanation for the correct option:

For better understanding draw the diagram according to the question:

In the diagram, we can see

Set $A=$segment $\left(x+y\right)$ and set $B=$segment $\left(y+z\right)$

Now, Set $\left(A-B\right)=$segment present in $A$ but not in $B$

$=x$

$\therefore A-(A-B)=(x+y)-x$

$=y$

$=A\cap B$ [$y$ is present in both $A$ and $B$]

Thus, $\mathit{A}\mathbf{}\mathbf{–}\mathbf{}\mathbf{(}\mathit{A}\mathbf{}\mathbf{–}\mathbf{}\mathit{B}\mathbf{)}\mathbf{}\mathbf{=}\mathbf{}\mathit{A}\mathbf{}\mathbf{\cap }\mathbf{}\mathit{B}$

Hence, Option ‘C’ is Correct.