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 $N$ denote the set of all natural numbers and $R$ be the relation on $N \times N$ defined by $(a, b)$ $R$ $(c, d)$ if $ad(b + c) = bc(a + d),$ then $R$ is

Let $R$ be a relation on the set $N$ be defined by $\{(x, y)| x, y \in N, 2x + y = 41\}$. Then $R$ 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 $5 ?$

Let $A = \{1, 2, 3, 4\}$ and $R$ be a relation in $A$ given by $R = \{(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1), (3, 1), (1, 3)\}$. Then $R$ is

A relation on the set $A\, = \,\{ x\,:\,\left| x \right|\, < \,3,\,x\, \in Z\} ,$ where $Z$ is the set of integers is defined by $R= \{(x, y) : y = \left| x \right|, x \ne  - 1\}$. Then the number of elements in the power set of $R$ is