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The given logical expression is \((p \land q) \leftrightarrow (\neg r \lor q)\), and we need to construct a truth table for this expression using "T" for true and "F" for false.

### Steps to construct the truth table:

1. **Identify variables**: We have three variables: \(p\), \(q\), and \(r\).
2. **Determine all possible combinations of truth values** for \(p\), \(q\), and \(r\) (since each variable can either be true or false, there are \(2^3 = 8\) possible combinations).
3. **Evaluate intermediate expressions**: Calculate the values for:
   - \(p \land q\) (the conjunction of \(p\) and \(q\)),
   - \(\neg r\) (the negation of \(r\)),
   - \(\neg r \lor q\) (the disjunction of \(\neg r\) and \(q\)),
   - Finally, evaluate the biconditional \((p \land q) \leftrightarrow (\neg r \lor q)\).

### Truth Table:

| \(p\) | \(q\) | \(r\) | \(p \land q\) | \(\neg r\) | \(\neg r \lor q\) | \((p \land q) \leftrightarrow (\neg r \lor q)\) |
|-------|-------|-------|---------------|------------|-------------------|----------------------------------------------|
|   T   |   T   |   T   |      T        |     F      |        T          |                    T                         |
|   T   |   T   |   F   |      T        |     T      |        T          |                    T                         |
|   T   |   F   |   T   |      F        |     F      |        F          |                    T                         |
|   T   |   F   |   F   |      F        |     T      |        T          |                    T                         |
|   F   |   T   |   T   |      F        |     F      |        T          |                    T                         |
|   F   |   T   |   F   |      F        |     T      |        T          |                    T                         |
|   F   |   F   |   T   |      F        |     F      |        F          |                    T                         |
|   F   |   F   |   F   |      F        |     T      |        T          |                    T                         |

### Explanation:
- The biconditional \(\leftrightarrow\) is true when both sides of the expression have the same truth value (either both true or both false).
- In this case, the truth table shows that the entire expression evaluates to true for all possible values of \(p\), \(q\), and \(r\).

Would you like more details or have any other questions?

Here are some follow-up questions:
1. What does the biconditional \(\leftrightarrow\) mean in logic?
2. How does the conjunction (\(\land\)) operator work with truth values?
3. Can you explain why the disjunction (\(\lor\)) is true if at least one operand is true?
4. Why does negation (\(\neg\)) flip the truth value of a variable?
5. How does the truth table change if we use a different logical connective instead of biconditional?

**Tip**: When constructing a truth table, always break down complex expressions into smaller parts and evaluate each step carefully!

Construct a truth table for (p ∧ q) ↔ (¬ r ∨ q). Use T for true and F for false.

Learn how to construct a truth table for the expression (p ∧ q) ↔ (¬ r ∨ q). This problem explores key concepts in propositional logic, including conjunction, disjunction, negation, and biconditional statements. Suitable for high school students studying logic.

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