If $n(A) = m$, then total number of reflexive relations that can be defined on $A$ is-

Let $\mathrm{T}$ be the set of all triangles in a plane with $\mathrm{R}$ a relation in $\mathrm{T}$ given by $\mathrm{R} =\left\{\left( \mathrm{T} _{1}, \mathrm{T} _{2}\right): \mathrm{T} _{1}\right.$ is congruent to $\left. \mathrm{T} _{2}\right\}$ . Show that $\mathrm{R}$ is an equivalence relation.

Show that the relation $R$ defined in the set A of all triangles as $R =\left\{\left( T _{1},\, T _{2}\right):\, T _{1}\right.$ is similar to $\left. T _{2}\right\}$, is equivalence relation. Consider three right angle triangles $T _{1}$ with sides $3,\,4,\,5, \,T _{2}$ with sides $5,\,12\,,13 $ and $T _{3}$ with sides $6,\,8,\,10 .$ Which triangles among $T _{1},\, T _{2}$ and $T _{3}$ are related?

Let $R$ be the relation in the set $N$ given by $R =\{(a,\, b)\,:\, a=b-2,\, b>6\} .$ Choose the correct answer.

Let $R$ and $S$ be two non-void relations on a set $A$. Which of the following statements is false

Let $\mathrm{A}=\{1,2,3,4\}$ and $\mathrm{R}=\{(1,2),(2,3),(1,4)\}$ be a relation on $\mathrm{A}$. Let $\mathrm{S}$ be the equivalence relation on $A$ such that $\mathrm{R} \subset \mathrm{S}$ and the number of elements in $\mathrm{S}$ is $\mathrm{n}$. Then, the minimum value of $\mathrm{n}$ is...............