Consider $f: X \rightarrow Y$, $y \in Y, A \subset X, B \subset Y$. The full preimage of $y$ is the set defined by {x ∈ X | f(x)= y}. Notation: $f^{−1}(y)$. The image of set $A \subset X$ is the set defined by {$f(x)$ | $x \in A$}. Notation: $f [A]$. The preimage of set $B \subset Y$ is the set defined by {$x \in X$ | $f(x) \in B$}. Notation: $f^{−1}[B]$.