Question

If $A=\{x,y\}$ and $B=\{3,4,5,7,9\}$ and $C=\{4,5,6,7\}$, find $A\times (B\cap C)$

• A. $\left\{\right(x,4),(x,5),(x,7),(y,4),(y,5),(y,7\left)\right\}$
• B. $\left\{\right(x,3),(x,5),(x,7),(y,4),(y,5),(y,7\left)\right\}$
• C. $\left\{\right(x,4),(x,5),(x,7),(y,4),(y,5),(y,9\left)\right\}$
• D. none of the above

Answer 1

Answer: (A)

$\left\{\right(x,4),(x,5),(x,7),(y,4),(y,5),(y,7\left)\right\}$

$B\cap C=\{3,4,5,7,9\}\cap \{4,5,6,7\}=\{4,5,7\}$
$\therefore A\times (B\cap C)=\{x,y\}\times \{4,5,7\}$
=$\left\{\right(x,4),(x,5),(x,7),(y,4),(y,5),(y,7\left)\right\}$