State whether the given statements are true or false
Truth value of `sqrt(3)` is not an irrational number is F

Answer

To determine whether the statement "The truth value of `sqrt(3)` is not an irrational number is F" is true or false, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Statement**:
The statement we need to evaluate is "The truth value of `sqrt(3)` is not an irrational number is F." Here, "F" means false.

2. **Identify the Nature of `sqrt(3)`**:
We know that `sqrt(3)` is the square root of 3. To determine if it is rational or irrational, we can recall that a number is considered irrational if it cannot be expressed as a fraction of two integers.

3. **Prove that `sqrt(3)` is Irrational**:
- Assume for contradiction that `sqrt(3)` is rational. This means we can express it as `p/q`, where `p` and `q` are integers with no common factors (in simplest form).
- Then, squaring both sides gives us `3 = p^2/q^2`, leading to `p^2 = 3q^2`.
- This implies that `p^2` is divisible by 3, and hence `p` must also be divisible by 3 (since 3 is a prime number).
- Let `p = 3k` for some integer `k`. Substituting back gives `p^2 = 9k^2`, so `9k^2 = 3q^2`, leading to `q^2 = 3k^2`.
- This implies that `q^2` is also divisible by 3, and thus `q` must also be divisible by 3.
- This contradicts our initial assumption that `p` and `q` have no common factors. Therefore, `sqrt(3)` cannot be expressed as a fraction of two integers, proving it is irrational.

4. **Evaluate the Original Statement**:
Since `sqrt(3)` is indeed an irrational number, the statement "The truth value of `sqrt(3)` is not an irrational number" is false.

5. **Conclusion**:
The truth value of the statement "The truth value of `sqrt(3)` is not an irrational number" is false (F). Therefore, the statement itself is true.

### Final Answer:
The statement is true.