A truth-function is a function whose arguments take true ($1$) or false ($0$) and return either true or false as their output.
- Formally, a truth-function is a function .
- Any well-formed formulae defines a truth-function and vice-versa.
- 2. Disjunctive Normal Form > Truth Table to DNF can be used to build the function.
title: Example
Let $f$ be the truth-function as defined:
$$
f(P,Q,R) = 1 \iff \text{either } P = Q = 0 \text{ or } Q = R = 1
$$
Hence $f$ is equal to $1$ in these four exact cases:
$$
f(0,0,0), f(0,0,1), f(0,1,1), f(1,1,1)
$$