Question

Let R = {(a, b): a = b²} for all a, b ∈ N.

Show that R satisfies none of reflexivity, symmetry and transitivity.

Answer 1

It is given that

R = {(a, b): a = b²} for all a, b ∈ N

Reflexivity-

By substituting 2 we get

2 ≠ 2² where 2 is not related to 2

It can be written as

(2, 2) ∉ R

Hence, R is not reflexive.

Symmetry-

By substituting 4 we get

4 = 2²

It can be written as

(4, 2) ∈ R and (2, 4) ∉ R

Hence, R is not symmetric.

Transitive-

Here, we know that (16, 4) ∈ R and (16, 2) ∉ R

Therefore, R is not transitive.