Question

Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}. The relation R is

• A. Reflexive
• B. Transitive
• C. Not symmetric
• D. A function

Answer 1

Answer: (C)

Not symmetric

Answer 2

Given A = {1, 2, 3, 4}

R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)}

(2, 3) ∈ R but (3, 2) ∉ R. Hence R is not symmetric.

R is not reflexive as (1, 1) ∉ R.

R is not a function as (2, 4) ∈ R and (2, 3) ∈ R.

R is not transitive as (1, 3) ∈ R and (3, 1) ∈ R but (1, 1) ∉ R.