Odisha Board Solutions for Chapter: Relations and Functions, Exercise 2: Exercises- 3(b)

Give an example of a relation $f$ such that

$domf=rngf$

Give an example of a relation $f$ such that

$domf\subset \mathrm{rng}f$

Give an example of a relation $f$ such that

$domf\supset \mathrm{rng}f$

Give an example of a relation $f$ such that

$f\cup f^{-1}=\varphi$

Give an example of a relation $f$ such that

$f=f^{-1}$

Give an example of a relation $f$ such that

$f\cap f^{-1}\ne \varphi$

Let $R=\left\{\left(a,a^3\right)\mid a\right.$ is a prime number less than $10\}$

Find (i) $R$ (ii) $\mathrm{domain} R$, (iii) $\mathrm{range} R$, (iv) $R^{-1}$, (v) $\mathrm{domain} R^{-1}$, (vi) $\mathrm{range} R^{-1}$

Let $A=\{1,2,3,4,6\}$ and Let $R$ be a relation on $A$ defined by $R=\left\{\right(a,b\left)\right|a$ divides $b\}$

Find (i) $R$ (ii) $\mathrm{domain} R$, (iii) $\mathrm{range} R$, (iv) $R^{-1}$, (v) $\mathrm{domain} R^{-1}$, (vi) $\mathrm{range} R^{-1}$