List 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}

Step 1: In the given problem we have to list the members of these sets.

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

Real number includes all types of numbers like rational , fractions , whole numbers etc.

For x2= 1

This is only possible by {-1,1}

Put x=-1

Then (-1)2=1

Similarly put =1

Then

(1)2=1

Therefore the set of x will be {-1,1}

Step 2:

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

Integers is defined as the number can be written positive, negative or zero also without fraction form.

For the given statement integer must be positive.Let suppose x be the positive natural numbers less than 12

Therefore, the set of x will be {1,2,3,4,5,6,7,8,9,10,11}