Question

If $A=\{1,2\}$, $B=\{2,3\}$ and $C=\{3,4\}$, then what is the cardinality of $(A\times B)\cap (A\times C)$

• A. $8$
• B. $6$
• C. $2$
• D. $1$

Answer 1

The correct option is C $2$

$A=\{1,2\}$, $B=\{2,3\}$ and $C=\{3,4\}$

Now, $A\times B=\left\{\right(1,2),(1,3),(2,2),(2,3\left)\right\}$

$A\times C=\left\{\right(1,3),(1,4),(2,3),(2,4\left)\right\}$ And

$(A\times B)\cap (A\times C)=\left\{\right(1,3),(2,3\left)\right\}$

So cardinality is $2$.

Hence, option C is correct.