Question

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

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

Answer 1

Answer: (A)

$A = \{x: x^2 - 5x + 6 = 0\}$
$x^2 - 5x + 6 = 0$
$\Rightarrow (x - 3) (x - 2) = 0$
$\Rightarrow x = 3, 2$
$\therefore A = \{3,2\}, B = \{2,4\}, C = \{4, 5\}$
Now, $B\cap C=\{4\}$
$\Rightarrow A \times \left(B \cap C\right)=\left\{3,2\right\}\times\left\{4\right\}$
$=\left\{\left(3, 4\right), \left(2, 4\right)\right\}$.