Question

If $A=\{x:x^2-5x+6=0\}$, $B=\{2,4\}$, $C=\{4,5\}$ then $A\times (B\cap C)$

• A. $\left\{\right(2,4),(3,4\left)\right\}$
• B. $\left\{\right(4,2),(4,3\left)\right\}$
• C. $\left\{\right(2,4),(3,4),(4,4\left)\right\}$
• D. $\left\{\right(2,4),(3,4),(4,4),(5,5\left)\right\}$

Answer 1

The correct option is A $\left\{\right(2,4),(3,4\left)\right\}$

$x^2-5x+6=0\Rightarrow (x-2)(x-3)=0;x=2,3$

$B\cap C=\left\{4\right\};A=\{2,3\}$

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

$=\left\{\right(2,4),(3,4\left)\right\}$