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:

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!