If $A = {x : x^{2} - 5 x + 6 = 0}, B = {2, 3}$ and $C = {2, 3, 3}$ then prove that $A = B = C$ .

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Solution

$A = {x : x^{2} - 5 x + 6 = 0}$
$= {x : x^{2} - 3 x - 2 x + 6 = 0}$
$= {x : (x - 2) (x - 3) = 0}$
$= {x : x = 2, 3} = {2, 3}$
Therefore, $A = B = C$ as $B = {2, 3}$ and $C = {2, 3, 3} = {2, 3}$

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