Logic algebras {Boolean algebra}| {extensional logic} can depend on set theory {logic of classes}.
operations
Rules for operating on sets are the same as logic rules. Boolean algebra uses the number zero as empty set for false and the number one as universal set for true. Boolean addition is set-theory selection operation. Boolean-algebra negation is set complement: -a = ~a = NOT a. Boolean-algebra addition is set union {inclusive OR, logic}: a + b = (a | b) = a OR b. Boolean-algebra subtraction is set intersection: a - b = (a & b) = a AND b.
laws
Boolean algebra follows set-theory contradiction, commutation, association, and distribution laws. Boolean algebra uses excluded-middle law.
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Date Modified: 2022.0224