If p is true and q is false, then `p implies q` is:

Options

A. True
B. False
C. p
D. `~| p`

Answer

To determine the truth value of the statement "P implies Q" when P is true and Q is false, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Implication**: The statement "P implies Q" (denoted as P → Q) means that if P is true, then Q must also be true for the implication to be true. If P is true and Q is false, the implication will be false.

2. **Set the Values**: We are given that P is true (T) and Q is false (F). Thus, we can represent this as:
- P = True (T)
- Q = False (F)

3. **Construct the Truth Table**: A truth table for the implication P → Q looks like this:

| P | Q | P → Q |
|-------|-------|-------|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |

From the truth table, we can see that:
- When P is true and Q is true, P → Q is true.
- When P is true and Q is false, P → Q is false.

4. **Evaluate the Given Condition**: Since we have P = T and Q = F, we look at the second row of the truth table. Here, P is true and Q is false, which gives us:
- P → Q = F (false)

5. **Conclusion**: Therefore, the value of "P implies Q" when P is true and Q is false is false.

### Final Answer:
The answer is **false**.

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