{xlx is an integer such that x

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QUESTION:

List of the members of these sets.

(a){x|x is a real number such that x2 = 1.}

(b){x|x is a positive integer less than 12}

(c){x|x is the square of an integer and x < 100}

(d){x|x is an integer such that x2 = 2}

SOUTION:

(a){x|x is a real number such that x2 = 1.}

$x=\sqrt 1=\plusmn1$

$=\{-1,1\}$

(b){x|x is a positive integer less than 12}

$=\{1,2,,3,4,5,6,7,8,9,10,11\}$

(c){x|x is the square of an integer and x < 100}

$=\{1,4,9,16,25,36,49,64,81\}$

(d){x|x is an integer such that x2 = 2}

$x=\plusmn \sqrt2$

But $x$ is an integer

$\sqrt2$ and $-\sqrt2$ are not integers

Therefore, there is no integer element that satisfies $x^2=2$

$=\emptyset$