Rule: Product

September, 2026

The product rule gives the size of a product of sets. Recall that if $P_{1}, P_{2}, \dots P_{n}$ are sets, then

P_{1} \times P_{2} \times \dots \times P_{n}

is the set of all sequences whose first term is drawn from $P_{1}$ , second from $P_{2}$ and so forth.

Theorem (Product rule). If $P_{1}, P_{2}, \dots, P_{n}$ are finite sets, then:

∣ P_{1} \times P_{2} \times \dots \times P_{n} ∣ = ∣ P_{1} ∣ \cdot ∣ P_{2} ∣ \dots ∣ P_{n} ∣

When to use

Rule of product should be applied whenever we chain counting, when things happen in order, one after another (or at the same time) - it translates to mathematical conjunction $\land$ .

Rule: Product

When to use

See also: