Domain and Range of a Relation

Topics: Discrete Mathematics

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(definition)

Let $R$ be a relation between $A$ and $B$. Given $a\in A$, $b\in B$, we define the domain of $R$ as:

$$\text{dom}(R)=\{a\mid \exists b\text{ such that }(a,b)\in R\}$$

We define the range of $R$ as:

$$\text{ran}(R)=\{b\mid \exists a\text{ such that }(a,b)\in R\}$$