Embibe Experts Solutions for Exercise 1: EXERCISE 1.1

Let $A$and $B$ be finite sets containing $m$ and $n$ elements respectively.The number of relations that can be defined from $A$ to $B$ is

Let $R_1$ and $R_2$ be equivalence relations on a set $A$, then $R_1\cup R_2$ may or may not be

Let $A=\{a,b,c\}$ and $R=\left\{\right(a,a),(b,b),(c,c),(b,c),(a,b\left)\right\}$ be a relation on $A$, then $R$ is

Let $O$ be the origin. If a relation $R$ is defined between two points $A$ and $B$ in a plane such that $OA=OB$. Then the relation$R$ is

Let $A=\{1,2,3\}$, which of the following relation is the smallest equivalence relation on the set $A$ ?

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

Let $A=\{1,2,3\}$, we define
(i) $R_1=\left\{\right(1,1),(2,2),(3,3\left)\right\}$
(ii) $R_2=\left\{\right(1,2),(2,1),(2,2),(1,1\left)\right\}$
(iii) $R_3=\left\{\right(1,2),(1,3\left)\right\}$
(iv) $R_4=\left\{\right(1,1),(3,3\left)\right\}$
(v) $R_5=A\times A$
then, which of the following is true?

If $R$ and $R^{\text{'}}$ are symmetric relations (not disjoint) on a set $A$, then the relation $R\cup R^{\text{'}}$ is