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The expression you provided is:

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

where:
- \( p \) and \( q \) represent statements,
- \( \lor \) is the logical OR,
- \( \neg \) is the logical NOT.

We'll construct a truth table for this expression. Since there are three variables \( p \), \( q \), and \( r \), the truth table will have \( 2^3 = 8 \) rows, covering all possible truth values for \( p \), \( q \), and \( r \).

Here is the step-by-step breakdown:

1. Compute \( p \lor q \).
2. Compute \( \neg p \).
3. Compute \( \neg r \).
4. Compute \( \neg p \lor \neg r \).
5. Finally, compute the full expression \( (p \lor q) \lor (\neg p \lor \neg r) \).

Let me now construct the full truth table.

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

Learn how to construct a truth table for the logical expression (p ∨ q) ∨ (~p ∨ ~r). This problem focuses on basic logic operations including OR and NOT, suitable for high school students. Step-by-step truth table construction with all possible truth values is included.

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