1.1 KiB
1.1 KiB
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Boolean algebra
Many of the laws that obtain in the mathematical realm of algebra also obtain for Boolean expressions.
The Commutative Law
x \land y = y \land x \
x \lor y = y \lor x
Compare the Commutative Law 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 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:
a \cdot (b + c) = a \cdot b + a \cdot c
In addition we have DeMorgan's Laws which express the relationship that obtains between the negations of conjunctive and disjunctive expressions