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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
Mentioned in:
Proofs: 1 2
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References
Bibliography
- Mendelson Elliott: "Theory and Problems of Boolean Algebra and Switching Circuits", McGraw-Hill Book Company, 1982