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The given compound statement is:

\[
(p \land q) \lor (p \to \neg q)
\]

We will construct a truth table to determine if this statement is a tautology (i.e., true for all possible truth values of \(p\) and \(q\)).

### Truth Table Setup:

We need columns for:
- \(p\)
- \(q\)
- \(p \land q\)
- \(\neg q\) (negation of \(q\))
- \(p \to \neg q\) (implication)
- The entire expression \((p \land q) \lor (p \to \neg q)\)

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

### Analysis:
- In all possible cases (rows), the final column (the compound statement) is true.

Since the compound statement is always true, **the given compound statement is a tautology**.

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the difference between a tautology and a contradiction?
2. How does an implication (\(p \to q\)) work in logic?
3. Can a compound statement be neither a tautology nor a contradiction?
4. How do logical connectives like \(\land\), \(\lor\), and \(\to\) function?
5. What other methods, besides truth tables, can be used to determine tautologies?

**Tip:** In logic, a statement is a tautology if it holds true under every possible combination of truth values for its components.

Use a truth table to determine whether the given compound statement is a tautology: (p ∧ q) ∨ (p → ¬q).

Learn how to use a truth table to check if the compound statement (p ∧ q) ∨ (p → ¬q) is a tautology. This problem involves logical connectives and the concept of tautology, suitable for high school students in Grades 10-12.

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