Consider the following statements:
A. The product of an integer and a rational number can never be a natural number.
B. The quotient of division of an integer by a rational number can never be an integer.
Which of the statements given above is /are correct?

Options

A. A only
B. B only
C. Both A and B
D. Neither A nor B.

Answer

To solve the problem, we need to analyze the two statements given:

**Statement A:** The product of an integer and a rational number can never be a natural number.

**Statement B:** The quotient of the division of an integer by a rational number can never be an integer.

We will evaluate each statement one by one.

### Step 1: Evaluate Statement A
1. **Choose an integer and a rational number.**
Let's take the integer \(4\) and the rational number \(2\) (which can be expressed as \(\frac{2}{1}\)).

2. **Calculate the product.**
The product of \(4\) (integer) and \(2\) (rational number) is:
\[ 4 \times 2 = 8 \]

3. **Check if the product is a natural number.**
The result \(8\) is indeed a natural number. Therefore, Statement A is false.

### Step 2: Evaluate Statement B
1. **Choose an integer and a rational number.**
Again, we will use the integer \(4\) and the rational number \(2\).

2. **Calculate the quotient.**
The quotient of \(4\) (integer) divided by \(2\) (rational number) is:
\[ \frac{4}{2} = 2 \]

3. **Check if the quotient is an integer.**
The result \(2\) is an integer. Therefore, Statement B is also false.

### Conclusion
Since both statements A and B are false, the correct answer is that neither statement is correct.

### Final Answer
The correct option is **D: Neither A nor B is correct.**

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