A compound statement with "OR" is false when

Options

A. At least one component statement is false
B. At most one component statement is false
C. All the component statements are false
D. Only one component statement is true other are false

Answer

To determine when a compound statement with "OR" is false, we can analyze the truth values of the statements involved. The "OR" operation is often denoted as \( A \lor B \), where \( A \) and \( B \) are two logical statements.

### Step-by-Step Solution:

1. **Understanding the "OR" Operation**:
The "OR" operation (denoted as \( A \lor B \)) is true if at least one of the statements \( A \) or \( B \) is true. It is only false when both statements are false.

2. **Creating a Truth Table**:
We can create a truth table to illustrate the possible truth values for \( A \) and \( B \):
- Let \( A \) and \( B \) be two logical statements.
- The possible truth values for \( A \) and \( B \) are:
- True (T)
- False (F)

The combinations are:
- \( A = T, B = T \) → \( A \lor B = T \)
- \( A = T, B = F \) → \( A \lor B = T \)
- \( A = F, B = T \) → \( A \lor B = T \)
- \( A = F, B = F \) → \( A \lor B = F \)

3. **Analyzing the Truth Table**:
From the truth table, we can summarize:
- \( A \lor B \) is true in three cases (when at least one of \( A \) or \( B \) is true).
- \( A \lor B \) is false only in one case (when both \( A \) and \( B \) are false).

4. **Conclusion**:
Therefore, a compound statement with "OR" is false when both component statements are false.

### Final Answer:
A compound statement with "OR" is false when both statements are false.

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