Any prime or compound propositions $\phi$ can be regarded as a function, called a Boolean function.

Lemma: Boolean Function

Let $\phi$ be a prime or a compound proposition containing exactly $n\ge 1$ prime propositions $p_1,\ldots,p_n$ with the interpretation $I$ and the corresponding valuation function $[[]]_I.$ Then $\phi$ represents a function $f_{\phi}:\mathbb B^n \to\mathbb B,$ where $\mathbb B$ is the set of truth values, defined as follows:

$$f_{\phi}(p_1,\ldots,p_n):=[[\phi]]_I=\cases{1&\text{if }I\models\phi,\\0&\text{if }I\not{\models}\;\phi.}$$

The function $f_\phi$ is called Boolean function of the proposition $\phi.$

Examples: 1 Proofs: 1

Chapters: 1
Corollaries: 2
Definitions: 3 4 5 6 7 8 9 10 11
Examples: 12
Lemmas: 13
Proofs: 14 15
Sections: 16

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