Truth Table Math Example 4

Follow the full solution, then compare it with the other examples linked below.

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Construct the truth table for

p \land \neg q

1
List the four combinations of $(p,q)$ : $(T,T)$ , $(T,F)$ , $(F,T)$ , $(F,F)$ . Then compute $\neg q$ : $F, T, F, T$ .
2
Now compute $p \land \neg q$ : $T \land F = F$ , $T \land T = T$ , $F \land F = F$ , $F \land T = F$ .

Answer

\begin{array}{cc|c} p & q & p \land \neg q \\ \hline T & T & F \\ T & F & T \\ F & T & F \\ F & F & F \end{array}

Truth tables evaluate compound statements row by row. Breaking the expression into smaller columns such as

\neg q

first makes the final column easier to compute accurately.

About Truth Table

A table that systematically lists every possible combination of truth values for the input variables and the resulting truth value of the expression.

Construct the truth table for [formula].

Build a truth table to verify that [formula] is logically equivalent to [formula].

Construct the truth table for [formula] and verify it equals [formula] (De Morgan's Law).