If $A = {x : x^{2} = 1}$ and $B = {x : x^{4} = 1}$ then $A △ B$ is equal to

{i, - i}

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{1, - 1}

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{- 1, 1, i, - i}

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{1, i}

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Solution

The correct option is A ${i, - i}$
$x^{2} = 1$
$\Rightarrow x = \pm 1$
And $x^{4} = 1$
$\Rightarrow x^{4} - 1 = 0$
$(x^{2} + 1) (x^{2} - 1) = 0$
$x = \pm i, \pm 1$
$A = {- 1, 1}, B = {- 1, 1, - i, i}$
$A - B = ϕ, B - A = {- i, i}$
$(A - B) \cup (B - A) = {- i, i} = A △ B$

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