Processing math: 100%

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.

Proofs: 1

Proofs: 1 2


Thank you to the contributors under CC BY-SA 4.0!

Github:
bookofproofs


References

Bibliography

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