The statement `p vv q` is

Options

A. a tautology
B. a contradiction
C. contingency
D. none of these

Answer

To determine whether the statement \( p \lor q \) (read as "p or q") is true or false, we can construct a truth table. The logical operator \( \lor \) (disjunction) is true if at least one of the operands is true. Let's break this down step by step.

### Step 1: Define the Variables
Let:
- \( p \) be a proposition that can be either true (T) or false (F).
- \( q \) be another proposition that can also be either true (T) or false (F).

### Step 2: Construct the Truth Table
We will create a truth table with all possible combinations of truth values for \( p \) and \( q \).

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

### Step 3: Analyze the Truth Table
- In the first row, both \( p \) and \( q \) are true, so \( p \lor q \) is true.
- In the second row, \( p \) is true and \( q \) is false, so \( p \lor q \) is still true.
- In the third row, \( p \) is false and \( q \) is true, so \( p \lor q \) is true.
- In the fourth row, both \( p \) and \( q \) are false, so \( p \lor q \) is false.

### Conclusion
The statement \( p \lor q \) is false only when both \( p \) and \( q \) are false, which occurs in the last row of the truth table.

### Final Answer
The statement \( p \lor q \) is false when both \( p \) and \( q \) are false.

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