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) not symmetric 

(b) transitive

(c) a function 

(d) reflexive.

Answer 1

(a) : R is a function as A = {1, 2, 3, 4} and (2, 4) ∈ R and (2, 3) ∈ R

R is not reflexive as (1, 1) ∉ R

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

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