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Lemma: De Morgan's Laws (Logic)

Let $x,y$ be two propositions. In the semantics of propositional logic, the following laws hold for the conjunction "$\wedge$", disjunction "$\vee$" and negation "$\neg$":

$$\begin{array}{c}\neg(x\vee y)=(\neg x)\wedge (\neg y),\\\neg(x\wedge y)=(\neg x)\vee (\neg y).\end{array}$$

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

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References

Bibliography

1. Mendelson Elliott: "Theory and Problems of Boolean Algebra and Switching Circuits", McGraw-Hill Book Company, 1982