The image you uploaded shows part of a truth table for a symbolic logical expression and a related question about determining the conditions for the compound statement to be true. The truth table has columns for the variables $p$, $q$, and $r$, along with intermediate expressions like $p \vee q$, $\neg r$, and $(p \vee q) \vee \neg r$.

To answer the question in part (c), we need to check under which conditions the compound statement $(p \vee q) \vee \neg r$ is true. Let me break this down for you:

Step-by-step analysis of the compound statement:

• We can look at each row in the truth table and evaluate the final expression $(p \vee q) \vee \neg r$.
• The final column shows whether the compound statement evaluates to true or false based on the values of $p$, $q$, and $r$.

Conditions for the statement to be true:

From the truth table, you can check the row(s) where the last column for $(p \vee q) \vee \neg r$ is true.

Now, referring to the image, the correct answer in part (c) is the set of conditions where the compound statement is true. By analyzing the truth table, it looks like the correct option is:

A. The statement is true when $p$ is false, $q$ is false, and $r$ is true.

Would you like more detailed steps on evaluating the truth table or any other clarification? Feel free to ask!

Further questions:

1. How do you evaluate logical OR ($\vee$) and NOT ($\neg$) operations in a truth table?
2. What is the significance of a truth table in propositional logic?
3. Can a truth table help you understand the validity of a logical argument?
4. How do you handle negations when constructing a truth table?
5. What are the possible truth values of a compound statement involving multiple variables?

Tip:

To ensure accuracy while evaluating truth tables, remember that the logical OR ($p \vee q$) is true when at least one of the variables is true, and the negation ($\neg r$) simply inverts the truth value of $r$.