Let $A$ be the non-void set of the children in a family. The relation $'x$ is a brother of $y'$ on $A$ is

The relation "is subset of" on the power set $P(A)$ of a set $A$ is

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 $A=\{1,2,3\} .$ Then number of relations containing $(1,2)$ and $(1,3)$ which are reflexive and symmetric but not transitive is

Let $R _{1}=\{( a , b ) \in N \times N :| a - b | \leq 13\}$ and $R _{2}=\{( a , b ) \in N \times N :| a - b | \neq 13\} .$ Thenon $N$

Let $R$ be a relation on $R$, given by $R=\{(a, b): 3 a-3 b+\sqrt{7}$ is an irrational number $\}$. Then $R$ is