Image and Preimage of a Function

Topics: Discrete Mathematics

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(definition)

Let $F:A\to B$ be a function and let $C\subseteq A$. The image of $C$ is defined as:

$$\text{im}(C)=\{F(a)\in B\mid a\in C\}$$

Now, let $E\subseteq B$. The preimage of $E$ is:

$$F^{-1}(E)=\{a\in A\mid F(a)\in E\}$$