Count of Rows of Truth Table

Theorem
Let $P$ be a statement form of propositional calculus.

Suppose $\mathcal P$ is of finite size such that it contains $n$ different letters.

Then a truth table constructed to express $P$ will contain $2^n$ lines.

Proof
In a truth table, one line is needed for each model of $P$.

The different letters used in $P$ can be considered to be its alphabet.

The result then follows from Number of Models for an Alphabet.