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Proof that ab is an arbitrary set in discrete mathematics ~(a∪b)= ~ a∪~ b
Use a' for non-A, and so on.

(A∪B)'=A'∩B '。

Proof: let x∈(A∪B)', then x does not belong to A∪B,

∴x does not belong to a, x does not belong to b,

∴x∈A'∩B'，

∴(A∪B)' is a subset of A'∩B'.

Similarly, it can be proved that A'∩B' is a subset of (A∪B)'.

∴(A∪B)'=A'∩B'.

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