Autosave: 2022-12-18 13:30:05

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