Question

If 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

The correct option is A

{(2, 4), (3, 4)}

Given, A = {$x:x^2-5x+6=0$}
$\therefore$ The elements of A are the roots of $x^2-5x+6=0$
$x^2-5x+6=0\Rightarrow (x-3)(x-2)=0\Rightarrow x=3\text{and}2$
$\therefore$ A = {2,3} , B = {2,4}, C = {4,5}

$\Rightarrow B\cap C$ = {4}

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