Give an example of a relation. Which is Reflexive and symmetric but not transitive.

Let $f: X \rightarrow Y$ be a function. Define a relation $R$ in $X$ given by $R =\{(a, b): f(a)=f(b)\} .$ Examine if $R$ is an equivalence relation.

Let $A=\{2,3,6,8,9,11\}$ and $B=\{1,4,5,10,15\}$

Let $\mathrm{R}$ be a relation on $\mathrm{A} \times \mathrm{B}$ define by $(\mathrm{a}, \mathrm{b}) \mathrm{R}(\mathrm{c}, \mathrm{d})$ if and only if $3 \mathrm{ad}-7 \mathrm{bc}$ is an even integer. Then the relation $\mathrm{R}$ is

Let $A$ be a set consisting of $10$ elements. The number of non-empty relations from $A$ to $A$ that are reflexive but not symmetric is

Let $R = \{ (3,\,3),\;(6,\;6),\;(9,\,9),\;(12,\,12),\;(6,\,12),\;(3,\,9),(3,\,12),\,(3,\,6)\} $ be a relation on the set $A = \{ 3,\,6,\,9,\,12\} $. The relation is