Embibe Experts Solutions for Chapter: Relations and Functions, Exercise 1: Madhya Pradesh Board-2019

Let $A=\{1,2,3\}$, then number of Equivalence relations containing $(1,2)$ is:

Show that relation '' is Equal to '' in sets is an Equivalence relation.

If $f\left(x\right)=x^2$and $g\left(x\right)=x+3, x\in R$, then find the value of $\left(gof\right)x,\left(fog\right)x·\left(fog\right)2$.

Let $A=\left\{1,2,3\right\}$. Then, number of relations containing $\left(1,2\right)$ and $\left(1,3\right)$, which are reflexive and symmetric but not transitive, is

Check whether the relation $R$ defined in the set $\left\{1,2,3,4,5,6\right\}$ as $R=\left\{\left(a,b\right):b=a+1\right\}$ is reflexive, symmetric or transitive.

Show that : $R\times R\to R$ defined by $a * b=a+2 b$ is neither commutative nor associative.