(related to Lemma: Boolean Function)
The Boolean constants $1$ and $0$ are particular types of prime propositions. They define constant Boolean functions $f(1)=1$ and $f(0)=0$.
A Boolean variable $x$ is another particular type of a prime proposition. They define an identity Boolean functions $$f(x)=x=\cases{0&\text{if }x=0,\\1&\text{if }x=1.}$$
Let \(f(x_1,x_2)\) be represented by the compound proposition \(x_1\vee \neg x_2\). Note that this proposition involves two connectives - the negation "$\neg$", which is an unary connective and the disjunction "$\vee$", which is a binary connective. The compound propositions involves two variables $x_1$ and $x_2$, which are prime propositions.
Using an interpretation $I$ and the corresponding valuation function $[[]]_I$ we can calculate the values of the Boolean function $f$ by assigning all possible truth values to the two variables of $f$: