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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:

| \( p \) | \( q \) | \( r \) | \( \neg p \) | \( q \lor \neg p \) | \( p \land (q \lor \neg p) \) | \([p \land (q \lor \neg p)] \lor r\) |
|:------:|:------:|:------:|:-----------:|:--------------------:|:----------------------------:|:-------------------------------------:|
| T      | T      | T      | F           | T                    | T                            | T                                     |
| T      | T      | F      | F           | T                    | T                            | T                                     |
| T      | F      | T      | F           | F                    | F                            | T                                     |
| T      | F      | F      | F           | F                    | F                            | F                                     |
| F      | T      | T      | T           | T                    | F                            | T                                     |
| F      | T      | F      | T           | T                    | F                            | F                                     |
| F      | F      | T      | T           | T                    | F                            | T                                     |
| F      | F      | F      | T           | T                    | F                            | F                                     |

### 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.

Construct a truth table for the given statement: [p ∧ (q ∨ ¬p)] ∨ r.

Explore the step-by-step construction of the truth table for the logical expression [p ∧ (q ∨ ¬p)] ∨ r. This problem covers key logic concepts including logical connectives AND, OR, and NOT, and is suitable for students in Grades 9-12.

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