The compound statement with. "And" is true when

Options

A. All its component statements are true
B. All its component statements are false
C. At least one component statement is true
D. None of these

Answer

To determine when a compound statement with "And" is true, we can analyze it using a truth table. Here’s a step-by-step solution:

### Step 1: Understand the "And" Operator
The "And" operator (denoted as ∧) is a logical conjunction that results in true only when both operands are true.

### Step 2: Create a Truth Table
We will create a truth table for two variables, A and B, to illustrate the behavior of the "And" operator.

| A | B | A ∧ B |
|-------|-------|-------|
| True | True | True |
| True | False | False |
| False | True | False |
| False | False | False |

### Step 3: Analyze the Truth Table
From the truth table, we can see:
- The output A ∧ B is true only when both A and B are true.
- In all other cases (when either A or B is false), the output is false.

### Step 4: Conclusion
Thus, a compound statement with "And" is true only when **all its component statements are true**.

### Final Answer
The compound statement with "And" is true when **all its component statements are true**.

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