Distributive law
Distributive law
is a name given to a number of laws of the same or similar form appearing in various disciplines — compare associative law. A distributive law of multiplication over addition appears in arithmetic
x X (y + z) = (x X y) + (x X z).
This distributive law holds also in the theory of real numbers, and in many other mathematical disciplines involving two operations called multiplication and addition. In the propositional calculus there are four distributive laws (two dually related pairs)
p[p ? r] = [pq ? pr].
[p ? qr] = [p ? q][p ? r].
p[p + r] = [pq + pr].
[p ? [q = r] = [p ? q] = [p ? r]].
Also four corresponding laws in the algebra of classes. — A.C.