If $A = {x : x i s a f a c t o r o f 5}, B = {x : x^{2} - 6 x + 5 = 0}$ , then what is the relation between $A$ and $B$ ?

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Solution

$A = {x : x is a factor of 5}$
Factors of $5 = 1, 5$
$A = {1, 5}$
$B = {x : x^{2} - 6 x + 5 = 0}$
$x^{2} - 6 x + 5 = 0$
$x^{2} - x - 5 x + 5 = 0$
$(x - 1) (x - 5) = 0$
$= 1, 5$
$B = {1, 5}$
As we know that if the two sets have exactly the same elements, then the two sets are equal.
Hence $A$ and $B$ are equal.

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