R S Aggarwal Solutions for Exercise 5: EXERCISE 2E

Find $a$ and $b$ when $\left(a-2b, 13\right)=\left(7, 2a-3b\right)$

Prove that $A\times B=B\times A\Rightarrow A=B$.

If $A=\left\{5\right\}$ and $B=\{5, 6\}$, write down all possible subsets of $A\times B$.

Let $R=\left\{\left(x,x^2\right): x \text{is a prime number less than} 10\right\}$

Write $R$ in roster form.

Let $R=\left\{\left(x,x^2\right): x \text{is a prime number less than} 10\right\}$

Find domain and range of $R$.

Let $A=\{1, 2, 3\}$ and $B=\left\{4\right\}$.

How many relations can be defined from $A$ to $B$?

Let $A=\{3, 4, 5, 6\}$ and $R=\left\{\right(a, b): a, b\in A$ and $a>b\}$.

Write $R$ in roster form.

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

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