Question

If $A=\{x:x-2=y,y<2,x,y\in W\}$ and $B=\{y:x+3=y,x<3,x,y\in W\},$ then

• A. $A=\{2,3\}$
• B. $B=\{3,4,5\}$
• C. $(A-B)\cap (B-A)=\varphi$
• D. $n\left(\right(A\Delta B)\times (B\Delta A\left)\right)=9$

Answer 1

Answer: (A), (B), (C), (D)

$n\left(\right(A\Delta B)\times (B\Delta A\left)\right)=9$

If $y<2\Rightarrow y=\{0,1\}$
$x-2=y\Rightarrow x-2=0\Rightarrow x=2$
$x-2=1\Rightarrow x=3$
$A=\{2,3\}$

Now, $x<3\Rightarrow x=\{0,1,2\}$
$x+3=y\Rightarrow 0+3=y\Rightarrow y=3$
$1+3=y\Rightarrow y=4$
$2+3=y\Rightarrow y=5$
$\therefore B=\{3,4,5\}$

Now, $A-B=\left\{2\right\},B-A=\{4,5\}$
$(A-B)\cap (B-A)=\varphi$
$A\Delta B=(A-B)\cup (B-A)$
$=\{2,4,5\}$
$n\left(\right(A\Delta B)\times (B\Delta A\left)\right)=3^2=9$