The relation $R= \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)\}$ on set $A = \{1, 2, 3\}$ is

$R$ is a relation from $\{11, 12, 13\}$ to $\{8, 10, 12\}$ defined by $y = x - 3$. Then ${R^{ - 1}}$ is

Let $R_{1}$ and $R_{2}$ be two relations defined on $R$ by $a R _{1} b \Leftrightarrow a b \geq 0$ and $a R_{2} b \Leftrightarrow a \geq b$, then

Let $A=\{1,2,3, \ldots \ldots .100\}$. Let $R$ be a relation on A defined by $(x, y) \in R$ if and only if $2 x=3 y$. Let $R_1$ be a symmetric relation on $A$ such that $\mathrm{R} \subset \mathrm{R}_1$ and the number of elements in $\mathrm{R}_1$ is $\mathrm{n}$. Then, the minimum value of $n$ is..........................

Show that the relation $R$ defined in the set $A$ of all polygons as $R=\left\{\left(P_{1}, P_{2}\right):\right.$ $P _{1}$ and $P _{2}$ have same number of sides $\}$, is an equivalence relation. What is the set of all elements in $A$ related to the right angle triangle $T$ with sides $3,\,4$ and $5 ?$

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