Let $X$ be a D17: Finite set such that

(i) | $E \subseteq X$ is a D78: Subset of $X$ |

Then
\begin{equation}
|X \setminus E|
= |X| - |E|
\end{equation}

Let $X$ be a D17: Finite set such that

(i) | $E \subseteq X$ is a D78: Subset of $X$ |

Then
\begin{equation}
|X \setminus E|
= |X| - |E|
\end{equation}

Subresults

▶ | R4188: Set cardinality in terms of finite ambient set |

Proofs

Let $X$ be a D17: Finite set such that

(i) | $E \subseteq X$ is a D78: Subset of $X$ |

Since $X$ is finite, result R477: Set finiteness is hereditary guarantees that also $E$ is finite. Hence, this result is a particular case of R1846: Cardinality of set complement. $\square$