Question

Let A = {1, 2, 3, 4} and let R = {(2, 2), (3, 3), (4, 4), (1, 2)} be a relation on A. Then R is ______.

Options

• reflexive

• symmetric

• transitive

• None of these

Answer 1

Let A = {1, 2, 3, 4} and let R = {(2, 2), (3, 3), (4, 4), (1, 2)} be a relation on A. Then R is transitive.

Explanation:

The relation R is not reflexive as

for 1 ∈ A, (1, 1) ∉ R

Similarly, R is not symmetric as

(1, 2) ∈ R but (2, 1) ∉ R

But R is transitive as:

(1, 2) ∈ R and (2, 2) ∈ R imply (1, 2) ∈ R.