Question

Let A = {0, 1, 2, 3 } and define a relation R as follows

R = {(0,0), (0,1), (0,3), (1,0), (1,1), (2,2), (3,0), (3,3)}.

Is R reflexive, symmetric and transitive ?

Answer 1

Given,

A = {0, 1, 2, 3}

(i) R is reflexive as (a,a) $\in$ R for every a $\in$ A.

(ii) R is symmetric, as (0,1) $\in$ R, (1,0) $\in$ R and (0,3) $\in$ R, (3,0) $\in$ R

(iii) R is not transitive as (3,0) (0,1) $\in$ R $⟹$ (3,1) does not exist in R.