R D Sharma Solutions for Chapter: Relation, Exercise 1: MULTIPLE CHOICE QUESTIONS (MCQs)

Let $A=\left\{1,2,3\right\}$ and consider the relation $R=\left\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\right\}$. Then, $R$ is _______________ .

The relation $S$ defined on the set $R$ of all real number by the rule $aSb$ if $a\ge b$ is _______________ .

The maximum number of equivalence relations on the set $A=\left\{1,2,3\right\}$ is _______________ 

Let $R$ be a relation on the set $N$ of natural numbers defined by $nRm$ if $n$ divides $m$. Then, $R$ is _____________ .

Let $S$ denote the set of all straight lines in a plane. Let a relation $R$ be defined by $aRb$ if $a$ is perpendicular to $b$ for all $a,b\in S$. Then, $R$ is ______________ .

Let $T$ be the set of all triangles in the Euclidean plane, and let a relation $R$ on $T$ be defined as $aRb$ if $a$ is congruent to $b$ for all $a, b\in T$. Then, $R$ is ____________ .

Consider a non-empty set consisting of children in a family and a relation $R$ defined as $aRb$ if $a$ is brother of $b$. Then, $R$ is _____________ .

For real numbers $x$ and $y$, define $xRy$ iff $\text{'}x-y+\sqrt{2}\text{'}$ is an irrational number. Then the relation $R$ is ___________ .