Question

Relation R defined on the set A={1,2,3,4} by R={(1,1),(2,2),(3,3)} is
a) reflexive
b) symmetric
c) transitive
d) none of these.

Answer 1

Question 1. Relation $R$ defined on the set $A = \{1,2,3,4\}$ by $R = \{(1,1),(2,2),(3,3)\}$ is

(a) reflexive;

(b) symmetric;

(c) transitive;

(d) none of these.

Solution. (a) It is not reflexive, because $(4,4)\not\in R$.

(b) It is symmetric, since for any $(a,b)\in R$ we have $a = b$, so $(b,a) = (a,b)\in R$.

(c) Let $(a,b),(b,c)\in R$. Then $a = b$ and $b = c$, therefore, $(a,c) = (a,b) = (b,c)\in R$.

Answer: $R$ is

(a) not reflexive;

(b) symmetric;

(c) transitive.