Statement -1 : Let `A={x` x is a prime numebr < 40 then number of different rational numbers whose numerator and denominator belong to A is 12.
because
Statement -2: `p/q` is a rational `Aq!=0` and `p,q epsilon I`

Options

A. Statement -1 is True, Statement-2 is True, Statement -2 is a correct explanation for Statement -1
B. Statement -1 is True, Statement -2 is True, Statemetn -2 is NOT a correct explanation for Statement -1.
C. Statement -1 is True, Statement -2 is False.
D. Statement -1 is False, Statement -2 is True

Answer

To analyze the statements, we need to evaluate each statement step by step.

### Step 1: Identify the prime numbers less than 40
The prime numbers less than 40 are:
- 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37

Counting these, we find there are a total of 12 prime numbers.

**Hint**: Remember that prime numbers are those greater than 1 that have no divisors other than 1 and themselves.

### Step 2: Determine the number of different rational numbers
A rational number can be expressed in the form \( \frac{p}{q} \), where \( p \) and \( q \) are integers, and \( q \neq 0 \). In this case, both \( p \) and \( q \) must be selected from the set of prime numbers \( A \).

1. **Choosing different primes for \( p \) and \( q \)**:
- We can choose \( p \) and \( q \) from the 12 prime numbers. The number of ways to choose 2 different primes from 12 is given by the combination formula \( \binom{n}{r} \):
\[ \binom{12}{2} = \frac{12 \times 11}{2 \times 1} = 66 \]
- Each pair \( (p, q) \) can yield two distinct rational numbers: \( \frac{p}{q} \) and \( \frac{q}{p} \).

So, the total number of different rational numbers from different primes is:
\[ 66 \times 2 = 132 \]

2. **Choosing the same prime for \( p \) and \( q \)**:
- If \( p = q \), then \( \frac{p}{q} = 1 \) for any prime \( p \). Since there are 12 primes, we have 12 additional rational numbers (one for each prime).

### Step 3: Total rational numbers
Now, we add the two cases together:
\[ 132 \text{ (from different primes)} + 12 \text{ (from same primes)} = 144 \]

### Conclusion
- **Statement 1**: The statement claims that the number of different rational numbers is 12, which is incorrect. The correct number is 144.
- **Statement 2**: This statement is true as it correctly defines the conditions for a rational number.

### Final Answer:
- Statement 1 is **false**.
- Statement 2 is **true**.