A compound statement with "OR" Is true when

Options

A. At least one component statement is true
B. AII the component statements are true
C. All the component statements are false
D. Both (1) & (2)

Answer

To determine when a compound statement with "OR" is true, we can analyze the logical expression and its truth table. Let's break down the solution step by step.

### Step-by-Step Solution:

1. **Understanding the Compound Statement**:
A compound statement with "OR" can be represented as \( A \lor B \), where \( A \) and \( B \) are individual statements.

2. **Truth Table Construction**:
We need to create a truth table for the compound statement \( A \lor B \). The truth values for \( A \) and \( B \) can either be true (T) or false (F).

| A | B | A ∨ B |
|-------|-------|-------|
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |

3. **Analyzing the Truth Table**:
- When both \( A \) and \( B \) are true (T, T), \( A \lor B \) is true (T).
- When \( A \) is true and \( B \) is false (T, F), \( A \lor B \) is true (T).
- When \( A \) is false and \( B \) is true (F, T), \( A \lor B \) is true (T).
- When both \( A \) and \( B \) are false (F, F), \( A \lor B \) is false (F).

4. **Conclusion**:
From the truth table, we can conclude that a compound statement with "OR" is true if:
- Both statements are true.
- At least one of the statements is true.

Thus, the answer is that a compound statement with "OR" is true when at least one of the component statements is true.