Which of the following statement is a tautology?

Options

A. (~p`vv`~q)`vv`(p`vv`~q)
B. (~p`vv`~q)`wedge` (p`vv`~q)
C. ~p`wedge`(~p`vv`~q)
D. ~q`wedge` (~p`vv`~q)

Explanation

To determine which of the given statements is a tautology, we can analyze the logical expressions provided. A tautology is a statement that is true in every possible interpretation.

### Step-by-Step Solution:

1. **Understanding Tautology**:
A tautology is a logical statement that is always true, regardless of the truth values of its components. Common examples include statements like \( P \lor \neg P \) (either P is true or not P is true).

2. **Identify the Statements**:
We need to analyze the statements provided in the options. Let's denote them as:
- Option A: \( \neg P \cup \neg Q \)
- Option B: \( P \cup \neg Q \)
- Option C: \( P \cap Q \)
- Option D: \( P \cup Q \)

3. **Analyzing Each Statement**:
- **Option A**: \( \neg P \cup \neg Q \)
- This statement is not a tautology because it can be false if both P and Q are true.
- **Option B**: \( P \cup \neg Q \)
- This statement is not a tautology because it can be false if P is false and Q is true.
- **Option C**: \( P \cap Q \)
- This statement is not a tautology because it can be false if either P or Q is false.
- **Option D**: \( P \cup Q \)
- This statement is a tautology because it is true if at least one of P or Q is true.

4. **Conclusion**:
After analyzing all the options, we find that **Option D: \( P \cup Q \)** is a tautology since it will always yield true regardless of the truth values of P and Q.

### Final Answer:
The statement that is a tautology is **Option D: \( P \cup Q \)**.