Skip to main content

Discrete Mathematical Structures

Dan Yasaki, Sebastian Pauli

Subsection 1.1.3 Truth tables

The truth table for a compound proposition gives the possible truth values of a compound proposition in terms of the truth values of the original propositions.
🔗

Remark 1.1.3.1.

In general, if a compound proposition involves \(k\) propositional variables, the truth table will have \(2^k\) rows.
🔗
🔗
The truth tables of the standard compound propositions are given in Figure 1.1.2.2, Figure 1.1.2.6, Figure 1.1.2.12, Figure 1.1.2.17, Figure 1.1.2.28, and Figure 1.1.2.29.
🔗

Example 1.1.3.2. Truth table for \((p\lor\lnot q) \implies (p\land q)\).

We construct the truth table of the compound proposition
\begin{equation*} (p\lor\lnot q) \implies (p\land q). \end{equation*}
🔗
Solution.
There are two propositional variables, so the table will have \(2^2 =4\) rows.
\begin{equation*} \begin{array}{|*{2}{c|}|*{4}{c|}} \hline p\amp q\amp \lnot q\amp p\lor\lnot q\amp p\land q\amp (p\lor\lnot q) n\implies (p\land q)\\ \hline \true \amp \true \amp \false \amp \true \amp \true \amp \true \\ \true \amp \false \amp \true \amp \true \amp \false \amp \false \\ \false \amp \true \amp \false \amp \false \amp \false \amp \true \\ \false \amp \false \amp \true \amp \true \amp \false \amp \false \\ \hline \end{array} \end{equation*}
🔗
🔗
🔗
🔗
PrevTopNext