Question

If $A=\{1,2,3\},B=\{3,4\},C=\{4,5,6\}$, then $(A\times B)\cap (B\times C)$ is equal to

• A. $\{1,4\}$
• B. $\{3,4\}$
• C. $\left\{\right(1,4),(3,4\left)\right\}$
• D. None of these

Answer 1

Answer: (B)

$\{3,4\}$

Given $A=\{1,2,3\},B=\{3,4\},C=\{4,5,6\}$

Therefore, $A\times B=\{1,2,3\}\times \{3,4\}$
$=\left\{\right(1,3),(1,4),(2,3),(2,4),(3,3),(3,4\left)\right\}$
and $B\times C=\{3,4\}\times \{4,5,6\}$
$=\left\{\right(3,4),(3,5),(3,6),(4,4),(4,5),(4,6\left)\right\}$
$\therefore (A\times B)\cap (B\times C)=\left\{\right(3,4\left)\right\}$