Let's solve the problem step by step.

The expression given is $(q \rightarrow p) \lor \sim r$, where:

• $q \rightarrow p$ is the implication (if $q$, then $p$).
• $\lor$ represents the logical OR.
• $\sim r$ represents the negation of $r$.

We'll construct the truth table for all possible combinations of $p$, $q$, and $r$. There are 3 variables, so we'll have $2^3 = 8$ rows.

Truth Table:

Explanation:

1. $q \rightarrow p$ is true if $q$ is false or $p$ is true (because an implication with a false antecedent is true, and if the consequent is true, the implication is true).
2. $\sim r$ negates the truth value of $r$.
3. The result of $(q \rightarrow p) \lor \sim r$ is true if at least one of $q \rightarrow p$ or $\sim r$ is true.

Would you like more details or have any questions?

Related Questions:

1. How do logical implications differ from other logical operations?
2. Can you construct a truth table for $(p \land \sim q) \lor r$?
3. What is the result of $q \rightarrow p$ when both $p$ and $q$ are false?
4. How does negation affect the outcome of a logical statement?
5. What are some practical uses of truth tables in computer science?

Tip:

To evaluate logical expressions, always start with inner operations (like negations) and then proceed to evaluate compound expressions step by step.