Disjoint sets/Moving/Bijection/Exercise

Let ${}M$ and ${}N$ be disjoint sets, and ${}x\in M$ Show that also ${}M\setminus \{x\}$ and ${}N\cup \{x\}$ are disjoint, and that

${}M\cup N={\left(M\setminus \{x\}\right)}\cup {\left(N\cup \{x\}\right)}\,$

holds.

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