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}
