Question

If $A=\{y:y={\log }_2|x-2|,x<5,x\text{is a whole number}\},B=\{y:y=|x-2|,x\in [0,1],y\in N\},C=\{1,3,5\}$
, then $n\left(\right(A\times B)\cap (B\times C\left)\right)$ is

• A. $0$
• B. $5$
• C. $1$
• D. $6$

Answer 1

The correct option is C $1$

${\log }_2|x-2|$ is not defined for $x=2$
now for $x=0,1,3,4$
$|x-2|=2,1,1,2$
$\therefore A=\{0,1\}$
$y=|x-2|,x\in [0,1]\Rightarrow y\in \{1,2\}(\because y\in N)\Rightarrow B=\{1,2\}C=\{1,3,5\}$

$(A\times B)\cap (B\times C)=(A\cap B)\times (B\cap C)$
$=\left\{\right(1,1\left)\right\}$