From aa3ba5196be2f40c778a2943912239dec4443c14 Mon Sep 17 00:00:00 2001 From: thomasabishop Date: Sun, 18 Dec 2022 13:30:05 +0000 Subject: [PATCH] Autosave: 2022-12-18 13:30:05 --- Logic/Propositional_logic/Boolean_algebra.md | 30 ++++++++++++++++++++ 1 file changed, 30 insertions(+) diff --git a/Logic/Propositional_logic/Boolean_algebra.md b/Logic/Propositional_logic/Boolean_algebra.md index f1e9383..4df4537 100644 --- a/Logic/Propositional_logic/Boolean_algebra.md +++ b/Logic/Propositional_logic/Boolean_algebra.md @@ -19,4 +19,34 @@ $$ x \lor y = y \lor x $$ +Compare the [Commutative Law](/Mathematics/Prealgebra/Whole_numbers.md#the-commutative-property) in the context of arithmetic. + ## The Associative Law + +$$ + x \land (y \land z) = (x \land y) \land z +$$ + +$$ + x \lor (y \lor z) = (x \lor y) \lor z +$$ + +Compare the [Associative Law](/Mathematics/Prealgebra/Whole_numbers.md#the-associative-property) in the context of arithmetic. + +## The Distributive Law + +$$ + x \land (y \lor z) = (x \land y) \lor (x \land z) +$$ + +$$ + x \lor (y \land z) = (x \lor y) \land (x \lor z) +$$ + +Compare for instance how this applies in the case of [multiplication](/Mathematics/Prealgebra/Distributivity.md): + +$$ + a \cdot (b + c) = a \cdot b + a \cdot c +$$ + +In addition we have [DeMorgan's Laws](/Logic/Laws_and_theorems.md/DeMorgan's_Laws.md) which express the relationship that obtains between the negations of conjunctive and disjunctive expressions