Give the truth value of each of the following statements.
If `4 + 5=9,` then 9-5=0.

Answer

To determine the truth value of the statement "If 4 + 5 = 9, then 9 - 5 = 0", we will analyze the components of the statement step by step.

### Step 1: Identify the components of the statement
Let:
- \( P \): The statement "4 + 5 = 9"
- \( Q \): The statement "9 - 5 = 0"

### Step 2: Determine the truth value of \( P \)
We evaluate \( P \):
- \( P \) is true because \( 4 + 5 = 9 \) is a correct mathematical statement.

### Step 3: Determine the truth value of \( Q \)
Next, we evaluate \( Q \):
- \( Q \) is false because \( 9 - 5 = 4 \), not 0.

### Step 4: Analyze the implication \( P \implies Q \)
The statement "If \( P \), then \( Q \)" can be written as \( P \implies Q \). The truth value of an implication is defined as follows:
- The implication \( P \implies Q \) is false only when \( P \) is true and \( Q \) is false.
- In all other cases (when \( P \) is false or both \( P \) and \( Q \) are true), the implication is true.

### Step 5: Apply the truth values to the implication
From our earlier steps:
- \( P \) is true.
- \( Q \) is false.

Since \( P \) is true and \( Q \) is false, we find that:
- \( P \implies Q \) is false.

### Conclusion
The truth value of the statement "If 4 + 5 = 9, then 9 - 5 = 0" is **false**.

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