Relation, Number of relation - Practice Questions & MCQ

A relation $R$ from a non-empty set $A$ to a non-empty set $B$ is a subset of the cartesian product $A \times B$.
The subset is derived by describing the relationship between the first element and the second element of the ordered pairs in $\mathrm{A} \times \mathrm{B}$.

The second element is called the image of the first element.
If the element $(a, b)$ belongs to $R$, (here $a$ belongs to $A$ and $b$ belongs to $B$ ), then the relation is represented as a R b.

Number of Relations from A to B
If $A$ has $m$ elements and $B$ has $n$ elements, then $A \times B$ has $m \times n$ elements.
As the number of subsets of $A x B$ is $2^{m n}$, and a relation is a subset of $A x B$, so the total number of relations from $A$ to $B$ will be $2^{\mathrm{mn}}$