To construct the truth table for the given logical expression:

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

We need to proceed step by step by evaluating each part separately. Let's go through the table:

Columns to be filled:

1. $\neg p$: Negation of $p$
2. $q \lor \neg p$: Logical OR between $q$ and $\neg p$
3. $p \land (q \lor \neg p)$: Logical AND between $p$ and $(q \lor \neg p)$
4. $[p \land (q \lor \neg p)] \lor r$: Logical OR between the previous result and $r$

Step-by-Step Solution:

Explanation:

1. $\neg p$ is just the opposite of $p$.
2. $q \lor \neg p$ is true if either $q$ is true or $\neg p$ is true.
3. $p \land (q \lor \neg p)$ is true if both $p$ and $(q \lor \neg p)$ are true.
4. Finally, $[p \land (q \lor \neg p)] \lor r$ is true if either $p \land (q \lor \neg p)$ or $r$ is true.

Would you like further details or explanations on any part?

Here are 5 related questions for practice:

1. How do you construct the truth table for $\neg(q \land r)$?
2. What would the truth table look like for $p \lor (q \land r)$?
3. Can you explain the logical equivalence between $p \lor q$ and $\neg p \rightarrow q$?
4. How do you determine if two logical expressions are equivalent using truth tables?
5. What does a tautology mean in terms of truth tables?

Tip: To check the validity of logical expressions, always start by breaking down each component and handling one logical operation at a time.