Embibe Experts Solutions for Chapter: Set Theory and Relations, Exercise 1: EXERCISE-1

$A$ and $B$ are two sets having $3$ and $4$ elements respectively and having $2$ elements in common. The number of relations which can be defined from $A$ to $B$ is

For $n,m\in N, n$ | $m$ means that $n$ is a factor of $m,$ the relation I is

Let $R=\left|\left(x,y\right):x,y\in A,x+y=5\right|$ where $A=\left\{1,2,3,4,5\right\}$ then

Let $x,y\in I$ and suppose that a relation $R$ on $I$ is defined by $x R y$ if and only if $x\le y$ then

Let $X$ be a family of sets and $R$ be a relation on $X$ defined by $\text{'}A$ is disjoint from $B\text{'}$. Then $R$ is

If $R$ be a relation $\text{'}<\text{'}$ from $A=\left\{1,2,3,4\right\}$ to $B=\left\{1,3,5\right\}$ i.e. $\left(a,b\right)\in R$ iff $a<b$, then $RO{R}^{-1}$ is

If $R$ ia an equivalence relation in a set $A,$ then $R^{-1}$ is

Let $R$ and $S$ be two equivalence relations in a set $A$. Then