Question

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

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

Answer 1

Answer: (A)

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