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Chapter 3: Problem 25

In Exercises 25-42, construct a truth table for the given statement. \(p \vee \sim q\)

Short Answer

Expert verified
The truth table for \(p \vee \sim q\) would have the following truth values in order of TT, TF, FT, FF, for \(p , q\): TT, TF, TT, FF.

Step by step solution

01

Set-up the truth table

Start by creating a table with three columns. Label the first two columns as \(p\) and \(q\), and the final column as \(p \vee \sim q\). Then list all possible combinations of truth values for \(p\) and \(q\) which is True (T) and False (F). These would be TT, TF, FT, FF.
02

Calculate the truth value of \(\sim q\)

Next, you determine the truth value of \(\sim q\) for each row of the truth table. Remember, \(\sim q\) inverses the truth value of \(q\). So, if \(q\) is True, \(\sim q\) will be False and vice versa.
03

Determine the truth value of \(p \vee \sim q\)

Now, for each row in the table, combine the truth values of \(p\) and \(\sim q\) using the OR operation. If either \(p\) or \(\sim q\) is True, then \(p \vee \sim q\) is True. If both are False, then \(p \vee \sim q\) is False. Complete the table by doing this for all rows.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Logical Disjunction
Logical disjunction is an important concept in the study of logic, particularly in truth tables. It is represented by the symbol \(\vee\) and is commonly known as the logical \

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