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Proposition: De Morgan's Laws (Sets)

Let $A,B$ be two sets. The following laws hold for the set intersection "$\cap$", set union "$\cup$" and set complent "$^C$":

$$\begin{array}{rcl}(A\cap B)^C&=&(A^C)\cup (B^C),\\(A\cup B)^C&=&(A^C)\cap (B^C).\end{array}$$

This law is named after Augustus De Morgan (1806 - 1871).

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References

Bibliography

  1. Kane, Jonathan: "Writing Proofs in Analysis", Springer, 2016