Question

Let, A = {(n, 2n): n ϵ N} and B = {(2n, 3n): n ϵ N}. What is (A ∩ B) equal to?
1. {(2n, 3n): n ϵ N}
2. {(n, 2n): n ϵ N}
3. {(2n, 5n): n ϵ N}
4. ϕ

Answer 1

Correct Answer - Option 4 : ϕ

Concept:

The intersection of two sets X and Y is the set of elements that are common to both set X and set Y. It is denoted by X ∩ Y and is read ‘X intersection Y ’

 

Calculation:

A = {(n, 2n): n ϵ N} when N is 1, 2, 3, ..........

= {(1, 2), (2, 4), (3, 6), ………} 

B = {(2n, 3n): n ϵ N} when N is 1, 2, 3, ..........

= {(2, 3), (4, 6), (6, 9), ………}

There is no member common to both the sets

 A ∩ B = ϕ

∴ A ∩ B has no set common.