Question

U ={1,2} A={x:x belongs to N,x^2+x-2 =0} a complement is​

Answer 1

SOLUTION

GIVEN

U = { 1 , 2 }

A = { x : x ∈ N : x² + x - 2 = 0 }

TO DETERMINE

The complement of A

EVALUATION

Here it is given that

U = { 1 , 2 }

A = { x : x ∈ N : x² + x - 2 = 0 }

$\sf{ {x}^{2} + x - 2 = 0}$

$\sf{ \implies \: {x}^{2} +2 x - x - 2 = 0}$

$\sf{ \implies \: (x + 2)(x - 1) = 0}$

$\sf{ \implies \: x = - 2 \: , \: 1}$

A = { - 2 , 1 }

∴ The complement of A

= A'

= U - A

= { 2 }

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