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The question asks to construct a truth table for the logical expression \( p \lor \sim p \) (read as "p or not p"). Let's break it down.

### Step 1: Analyze the Expression
- \( p \) is a statement that can either be true (T) or false (F).
- \( \sim p \) represents the negation of \( p \). If \( p \) is true, then \( \sim p \) is false, and vice versa.
- \( p \lor \sim p \) is the logical OR between \( p \) and its negation.

### Step 2: Construct the Truth Table
Let's create a truth table for \( p \lor \sim p \):

| \( p \) | \( \sim p \) | \( p \lor \sim p \) |
|--------|-------------|--------------------|
|   T    |      F      |         T          |
|   F    |      T      |         T          |

- When \( p \) is True, \( \sim p \) is False, but since \( p \lor \sim p \) only needs one of them to be true, the result is True.
- When \( p \) is False, \( \sim p \) is True, so again \( p \lor \sim p \) is True.

### Step 3: Interpretation
This is an example of a **tautology**—the result is always true, regardless of the truth value of \( p \).

Thus, the correct answer is **(a) Tautology**.

Let me know if you'd like more details or have further questions! Here are some related questions:

1. What is the difference between a tautology and a contradiction?
2. Can you provide an example of a logical contradiction?
3. How does a disjoint relationship differ from logical equivalence?
4. What role do logical connectives like "OR" and "NOT" play in constructing truth tables?
5. How would the truth table change if we used \( p \land \sim p \) (AND instead of OR)?

**Tip:** Tautologies are logical statements that are always true, which makes them useful for proving other logical theorems!

Construct a truth table for p ∨ ~p. What word describes the outcome?

Learn how to construct a truth table for the logical expression p ∨ ~p and understand why it results in a tautology. This problem covers key concepts in logic, including logical OR and negation, and is suitable for high school students in grades 9-12.

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