Question

List the members of these sets.

Answer 1

a.{x | x is a real number such that x^2 = 1}

x^2 = 1 => x = +/- 1

=> {-1, 1} <------ answer

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

1 ≤ x < 12 => {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} <------ answer

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

x = n^2 < 100 => n^2 - 100 < 0

=> (n - 10) (n + 10) < 0

=> a) n - 10 > 0 and n + 10 < 0  => n > 10 and n < - 10 which is not possible

b) n - 10 < 0 and n + 10 > 0 => n < 10 and n > - 10 => - 10 < n < 10

=> n = { - 9, - 8, - 7, - 6, - 5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

=> x = {0, 1, 4, 9, 16, 25, 36, 49, 64, 81} <---- answer

d.{x | x is an integer such that x^2 = 2}

x =  {∅ } because x is √2 which is not an interger but an irrational number

=> Answer: { ∅ }