Question

If $A=\{x,y,z\}$ then the relation $R=\left\{\right(x,x),(y,y),(z,z),(z,x),(z,y\left)\right\}$ is ____

• A. symmetric
• B. transitive
• C. None of these
• D. Both $A$ and $B$

Answer 1

The correct option is B transitive

A relation $R$ in $A$ is said to be symmetric, if $(a,b)\in R⟹(b,a)\in R$ for $a,b\in A$.

Here $(z,x)\in R$. But $(x,z)\notin R$. Hence the relation is not symmetric.

A relation $R$ in $A$ is said to be transitive, if $(a,b)\in R$ and $(b,c)\in R⟹(a,c)\in R$ for all $a,b,c\in A$.

Here $(z,x)\in R$ and $(x,x)\in R⟹(z,x)\in R$.

Also $(z,y)\in R$ and $(y,y)\in R⟹(z,y)\in R$.

Hence relation is transitive.