Let's construct the truth table for the given logical statement:

$[p \land (q \lor \neg p)] \lor r$

To solve this, we will evaluate step by step. The columns you need to fill are:

1. $\neg p$ (the negation of $p$)
2. $q \lor \neg p$ (the disjunction of $q$ and $\neg p$)
3. $p \land (q \lor \neg p)$ (the conjunction of $p$ with the previous result)
4. $[p \land (q \lor \neg p)] \lor r$ (the final disjunction with $r$)

Let's break this down row by row, based on all possible truth values for $p$, $q$, and $r$ (True = T, False = F):

Detailed Explanation:

1. $\neg p$ is just the negation of $p$.
2. $q \lor \neg p$ combines the value of $q$ and the negation of $p$ using logical "or."
3. $p \land (q \lor \neg p)$ takes the value of $p$ and the result of $q \lor \neg p$ using logical "and."
4. $[p \land (q \lor \neg p)] \lor r$ combines the previous result with $r$ using logical "or."

Would you like a more detailed explanation or have any questions about this?

Here are 5 follow-up questions related to this topic:

1. How do you determine the negation of a variable in a truth table?
2. What is the difference between conjunction ($\land$) and disjunction ($\lor$)?
3. How do you know when a complex statement is true or false?
4. Can you find a scenario where a complex logical statement simplifies to a single truth value?
5. How would the truth table change if one of the operators was replaced with a conditional (→)?

Tip: Breaking complex logical statements into smaller components can make evaluating them easier, especially when building truth tables.