Question

List the members of these sets.

(a) {x | x is a real number such that x

2 = 5}

(b) {x | x is a positive integer less than 15}

(c) {x | x is the square of an integer and x < 200}

(d) {x | x is an integer such that x

2 = 5}

Answer 1

Let us list the members of these sets.

(a) $A=\{x | x\text{ is a real number such that }x^2 = 5\}$

It follows that $A=\{-\sqrt{5},\sqrt{5}\}.$

(b) $B=\{x | x\text{ is a positive integer less than 15}\}$

It follows that $B=\{1,2,3,4,5,6,7,8,9,10,11,12,13,14\}.$

(c) $C=\{x | x\text{ is the square of an integer and }x < 200\}$

It follows that $C=\{0,1,4,9,16,25,36,49,64,81,100,121,144,169,196\}.$

(d) $D=\{x | x\text{ is an integer such that }x^2 = 5\}$

Since the equation $x^2=5$ has no integer roots, $D=\emptyset.$