Answer to Question #159488 in Discrete Mathematics for Harsh

Question

List the members of these sets:

(a) A={ x∣x is a real number ∋ x2=1}

(b) B={ x∣x is a positive integer less than 100 }

(c) C={ x∣x is the square of an integer and x <100 }

(d) D={ x∣x is an integer ∋ x2=2 }

Answer 1

(a) x²=1 implies 0 = x²-1=(x-1)(x+1) and, hence, x=1 or x=-1. Therefore, A={1,-1}

(b) B={ x∣x is a positive integer less than 100 } = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99}

(c) C={ x∣x is the square of an integer and x <100 } = {0², 1², 2², 3², 4², 5², 6², 7², 8², 9²} = {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}

(d) $D=\{x\in \mathbb{Z}: x^2 = 2\} = \emptyset$ , because of |x| must be less than 2 and greater than 1, but no one integer satisfies to this conditions.