Write T before each true statement and write F before each false statement. Then give the truth value of the conditional expressed.
If 51 is the product of 17 and -3, then lions can fly in the air.

Answer

To solve the given problem, we need to analyze the statements and determine their truth values.

### Step 1: Identify the statements
Let:
- Statement \( p \): "51 is the product of 17 and -3"
- Statement \( q \): "Lions can fly in the air"

### Step 2: Determine the truth value of statement \( p \)
We calculate the product of 17 and -3:
\[ 17 \times -3 = -51 \]
Since \( p \) states that 51 is the product, and we found that the product is -51, statement \( p \) is **false**.

### Step 3: Determine the truth value of statement \( q \)
The statement \( q \) claims that "lions can fly in the air." This is not true, as lions are terrestrial animals and cannot fly. Therefore, statement \( q \) is also **false**.

### Step 4: Write the truth values before each statement
- For statement \( p \): F (false)
- For statement \( q \): F (false)

### Step 5: Analyze the conditional statement
The conditional statement is expressed as \( p \implies q \) (if \( p \), then \( q \)). In logic, a conditional statement is only false when the first part (antecedent) is true and the second part (consequent) is false.

Since both \( p \) and \( q \) are false, the conditional \( p \implies q \) is considered **true**. In logical terms, a false antecedent makes the entire conditional statement true regardless of the truth value of the consequent.

### Conclusion
- The truth values are:
- \( p \): F
- \( q \): F
- The truth value of the conditional \( p \implies q \) is **true**.

### Final Answer
- F (for statement \( p \))
- F (for statement \( q \))
- Truth value of \( p \implies q \): T (true)

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