Conjunction (Primitive Recursion)

Definition

Conjunction ( Primitive Recursion)

With representing false and representing true, conjunction is represented by the primitive-recursive function

On Boolean inputs , the product is exactly when both inputs are , and otherwise. This uses multiplication directly; outside Boolean inputs, the product need not be a truth value.

Construction

A false input contributes a zero factor, making the product . If both inputs are true, the product is . No further recursion or composition is needed.

Example

Conjunction as multiplication