# True or False: Let R={(3,1),(1,3),(3,3)} be a relation defined on the set A={1,2,3}.Then R is symmetric,transitive but not reflexive.

Toolbox:
• 1. A relation R defined on A is reflexive if $(a,a) \in R \qquad a \in A$
• 2. A relation R is symmetric if $(a,b) \in R=>(b,a) \in R \qquad a,b \in A$
• 3. A relation R is transitive if $(a,b) \in R,(b,c) \in R =>(a,c) \in R \qquad a,b,c \in A$
$R=\{(3,1),(1,3),(3,3)\} \qquad A=\{1,2,3\}$

$(1,1)(2,2) \in R$

Therefore R is not reflexive

$(3,1) \in R => (1,3) \in R$

R is symmetric

$(3,1) \in R$ but there does not exists

$(1,2) or (1,4) \in R$

So R is not transitive

Hence R is symmetric but neither transitive nor reflexive

$'False'$