If $A = \left\{ {1,2,3,......m} \right\},$ then total number of reflexive relations that can be defined from $A \to A$ is 

Let $R= \{(3, 3) (5, 5), (9, 9), (12, 12), (5, 12), (3, 9), (3, 12), (3, 5)\}$ be a relation on the set $A= \{3, 5, 9, 12\}.$ Then, $R$ is

Let $X =\{1,2,3,4,5,6,7,8,9\} .$ Let $R _{1}$ be a relation in $X$ given by $R _{1}=\{(x, y): x-y$ is divisible by $3\}$ and $R _{2}$ be another relation on $X$ given by ${R_2} = \{ (x,y):\{ x,y\}  \subset \{ 1,4,7\} \} $ or $\{x, y\} \subset\{2,5,8\} $ or $\{x, y\} \subset\{3,6,9\}\} .$ Show that $R _{1}= R _{2}$.

Show that the relation $R$ in the set $\{1,2,3\}$ given by $R =\{(1,2),(2,1)\}$ is symmetric but neither reflexive nor transitive.

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

Let $X$ be a family of sets and $R$ be a relation on $X$ defined by $‘A$ is disjoint from $B’$. Then $R$ is