R D Sharma Solutions for Chapter: Relation, Exercise 1: EXERCISE

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

Let $\mathrm{R}$ be relation defined on the set of natural number $\mathrm{N}$ as follows: $\mathrm{R}=\left\{\right(x,y):x\in \mathrm{N},y\in \mathrm{N},2x+y=41\}$.

Find the domain and range of the relation $\mathrm{R}$. Also verify whether $\mathrm{R}$ is reflexive, symmetric and transitive.

Is it true that every relation which is symmetric and transitive is also reflexive? Give reasons.

Show that the relation $\text{'}\ge \text{'}$ on the set $R$of all real numbers is reflexive and transitive but not symmetric ?

Give an example of a relation which is reflexive and symmetric but not transitive ?

Let $A =\{a,b,c\}$ and the relation $R$ be defined on $A$ as follows: $R=\left\{(a,a),(b,c),(a,b)\right\}$. Then, write minimum number of ordered pairs to be added in $R$ to make it reflexive and transitive.

Defines a relation on $N:$ $x+y= 10,x,y\in N$

Determine the above relation is reflexive, symmetric and transitive.

Defines a relation on $N:$ $xy$ is square of an integer, $x,y\in N$

Determine the above relation is reflexive, symmetric and transitive.