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Define a relation on a set. What do you mean by the domain and range of a relation? Give an example.

Solution:

Relation:
Suppose $P$ and $Q$ are two sets. Therefore, a relation $R$ from $P$ to $Q$ is a subset of $P \times Q$.
Therefore, $\mathrm{R}$ is a relation to $\mathrm{P}$ to $\mathrm{Q} \Leftrightarrow \mathrm{R} \subseteq \mathrm{P} \times \mathrm{Q}$, if $(\mathrm{p}, \mathrm{q}) \in \mathrm{R}$, it can be said that, ‘$\mathrm{p}$ is related to $\mathrm{q}$’, and it can be written as, ‘$\mathrm{p} \mathrm{R} \mathrm{q}$’.
And if $(\mathrm{p}$,q) $\notin R$, it can be said that ‘ $\mathrm{p}$ is not related to $\mathrm{q}$ ‘ and it can be written as ‘p $\mathrm{R}$ q’.

Domain:
Set of all the first elements or $\mathrm{x}$-coordinates of the ordered pairs is called Domain.

Range:
Set of all the second elements or $y$-coordinates of the ordered pairs
is called Range.