Question

Given the universal set = {x : x ∈ N and x < 20}, find :
A = {x : x = 3p ; p ∈ N}

Answer 1

Universal set = {x : x ∈ N and x < 20}
= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,....,19}

A = {x : x = 3p ; p ∈ N}
x = 3p

When p = 1,
x = 3 x 1
= 3
When p = 2,
x = 3 x 2
= 6
When p = 3,
x = 3 x 3
= 9
When p = 4,
x = 3 x 4
= 12
When p = 5,
x = 3 x 5
=15
When p = 6,
x = 3 x 6
= 18
∴  A = {3, 6, 9, 12, 15, 18}