Frontier Software


By Robert Laing

2 Value Algebra

Since conjunction is closely associated with the word and, it jarred me a bit to discover that it is logic’s equivalent of multiplication, while disjunction — commonly thought of as or — is logic’s addition, the arithmetic operator I associate with and.

Why conjunction equates to multiplication is best illustrated by its truth table:

pqp · q

Moving from binary to any number of propositions, the universal quantification symbol ∀(p) tends to be used, as in

∀(p) = p1 · p2 · … · pn

Laws Analogous to Arithmetic

  1. The commutative law for AND: pq ≡ qp
  2. The associative law for AND: p(qr) ≡ (pq)r
  3. The distributive law of AND over OR: p(q + r) ≡ (pq + pr)
  4. 1 (TRUE) is the identity for AND: (p AND 1) ≡ p
  5. 0 is the annihilator for AND: (p AND 0) ≡ 0

How conjunction differs from multiplication

  1. The distributive law for OR over AND: (p + qr) ≡ ((p + q)(p + r))
  2. Idempotence of AND: pp ≡ p