Question

Let A = {x : x = 6n∈N) and B = {x : x = 9n, n ϵ N}, find A ∩ B.

Answer 1

A = {x : x = 6n ∀ n ∈ N) 

As x = 6n hence for n = 1, 2, 3, 4, 5, 6… x = 6, 12, 18, 24, 30, 36… 

Hence A = {6, 12, 18, 24, 30, 36…} 

B = {x : x = 9n ∀ n ∈ N) 

As x = 9n hence for n = 1, 2, 3, 4… x = 9, 18, 27, 36… 

Hence B = {9, 18, 27, 36…} 

A ∩ B means common elements to both sets 

The common elements are 18, 36, 54, … 

Hence A ∩ B = {18, 36, 54, …} 

All the elements are multiple of 18 

Hence A ∩ B = {x: x = 18n ∀ n ∈ N}