Question

A relation on the set A = {x : |x| < 3, x ∈ Z}, where Z is the set of integers is defined by R = {(x, y) : y = |x| ≠ –1}. Then the number of elements in the power set of R is ______.

Options

• 32

• 16

• 8

• 64

Answer 1

A relation on the set A = {x : |x| < 3, x ∈ Z}, where Z is the set of integers is defined by R = {(x, y) : y = |x| ≠ –1}. Then the number of elements in the power set of R is 16.

Explanation:

A = {x : |x| < 3, x ∈ Z}

A= {–2, –1, 0, 1, 2} ; R = {(x, y) : y = |x|, x ≠ –1}

R = {(–2, 2), (0, 0), (1, 1), (2, 2)}

R has four elements

Number of elements in the power set of R = 2⁴ = 16