R S Aggarwal Solutions for Exercise 4: EXERCISE 2D

Let $A=\{2, 3, 5\}$ and $R=\left\{\right(2, 3), (2, 5), (3, 3), (3, 5\left)\right\}$

Find domain and range of $R$.

Let $A=\{0, 1, 2, 3, 4, 5, 6, 7, 8\}$ and let $R=\left\{\right(a, b): a, b\in A$ and $2a+3b=12\}$.

Find its domain and range.

Let $R=\left\{\right(a, b):a, b\in W$ and $3a+2b=15\}$, where $W$ is the set of whole numbers.

Show that Domain$\left(R\right)=$range$\left(R^{-1}\right)$

Let $R=\left\{\right(x, y): x, y\in Z$ and $\left.x^2+y^2=25\right\}$.

Express $R$ and $R^{-1}$ as sets of ordered pairs. Show that $R=R^{-1}$.

Find $R^{-1}$, when $R=\left\{\right(1, 2), (1, 3), (2, 3), (3, 2), (4, 5\left)\right\}$,

Find $R^{-1}$, when $R=\left\{\right(x, y): x, y\in N, x+2y=8\}$.

Let $A=\{a, b\}$. List all relations on $A$.

Let $R=\left\{\right(a, b): a, b\in N$ and $a<b\}$.

Show that $R$ is a binary relation on $N$, which is neither reflexive nor symmetric.