Let $R = \{(1, 3), (2, 2), (3, 2)\}$ and $S = \{(2, 1), (3, 2), (2, 3)\}$ be two relations on set $A = \{1, 2, 3\}$. Then $RoS =$
$\{(1, 3), (2, 2), (3, 2), (2, 1), (2, 3)\}$
$\{(3, 2), (1, 3)\}$
$\{(2, 3), (3, 2), (2, 2)\}$
$\{(2, 3), (3, 2)\}$
Determine whether each of the following relations are reflexive, symmetric and transitive:
Relation $\mathrm{R}$ in the set $\mathrm{N}$ of natural numbers defined as
$\mathrm{R}=\{(x, y): y=x+5 $ and $ x<4\}$
The minimum number of elements that must be added to the relation $R =\{( a , b ),( b , c )\}$ on the set $\{a, b, c\}$ so that it becomes symmetric and transitive is:
Give an example of a relation. Which is Symmetric and transitive but not reflexive.
Which one of the following relations on $R$ is an equivalence relation
The relation $R$ defined on a set $A$ is antisymmetric if $(a,\,b) \in R \Rightarrow (b,\,a) \in R$ for