M L Aggarwal Solutions for Chapter: Relations and Functions, Exercise 2: EXERCISE 2.2

If $A=\left\{2,3,6,10\right\} \text{and }B=\left\{1,6,10\right\}$, find the elements of the subset of $A\times B$ corresponding to the relation $R$ 'is less than'. Also represent this relation by an arrow diagram. 

Let $A=\{-2,-1,0,1,2\}$, list the ordered pairs satisfying the relation on $A$ 'is the square of '

Let $A=\{-2,-1,0,1,2\}$, list the ordered pairs satisfying the relation on $A$ 'is the negative of '

If $A=\{1,3,5,6\}$ and $B=\{3,4,5\}$, write the relation $R$ as a set of ordered pairs if $R=\{\left(x,y\right):\left(x,y\right)\in A\times B:x+y\text{ is even }\}$.

If $A=\{1,3,5,6\}$ and $B=\{3,4,5\}$, write the relation $R$ as a set of ordered pairs if $R=\left\{\left(x,y\right):\left(x,y\right)\in A\times B:xy\text{ is odd }\right\}$.

Let $R=\left\{\right(x,y):x,y\in Z,y=2x-4\}$. If $(a,-2) \mathrm{and} \left(4,b^2\right)$ belong to $R$, find the values of $a$ and $b$.

Find the linear relation between the components of the ordered pairs of the relation $R$  where, $R=\left\{\right(-1,-1),(0,2),(1,5),\dots \}$.

Find the linear relation between the components of the ordered pairs of the relation $R$  where, $R=\left\{\right(0,2),(-1,5),(2,-4),\dots \}$.