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Lemma: Distributivity of Conjunction and Disjunction

For all propositions \(x,y,z\) the following rules are tautological:

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

In other words, the conjunction "$\wedge$" and the disjunction "$\vee$" are distributive over each other.

Table of Contents

Proofs: 1

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Proofs: 1 2

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References

Bibliography

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