After we have explained what Boolean functions and what truth tables are, it is time to use these concepts to introduce important examples of connectives.
Let \(L\) be a set of propositions with the interpretation $I$ and the corresponding valuation function $[[]]_I$. A negation "\(\neg\)" is a Boolean function. \[\neg :=\begin{cases}L & \mapsto L \\ x &\mapsto \neg x \\ \end{cases}\]
defined by the following truth table:
Truth Table of the Negation
$[[x]]_I$ | $[[\neg x]]_I$ |
---|---|
\(1\) | \(0\) |
\(0\) | \(1\) |
Branches: 1
Corollaries: 2 3
Definitions: 4 5 6 7
Examples: 8
Explanations: 9
Lemmas: 10 11 12 13 14 15 16
Parts: 17
Proofs: 18 19 20 21 22 23 24 25 26