State 'T' for true and 'F' for false .
I. If a whole number is divided by another whole number which is greater than the first one, then the quotient is not equal to zero .
II. Sum of two whole numbers is always less than their product .
III. Whole numbers are not closed under multiplication .

Options

A. `{:(I,II,III),(T,T,T):}`
B. `{:(I,II,III),(T,F,F):}`
C. `{:(I,II,III),(T,T,F):}`
D. `{:(I,II,III),(F,T,T):}`

Answer

Let's analyze each statement one by one to determine if they are true (T) or false (F).

### Statement I:
"If a whole number is divided by another whole number which is greater than the first one, then the quotient is not equal to zero."

**Analysis:**
- Let's take an example. If we divide 3 (a whole number) by 5 (another whole number that is greater than 3), we get:
\[ \frac{3}{5} = 0.6 \]
The quotient is not a whole number, but it is not equal to zero. However, if we consider the case of whole number division, if we divide 3 by 5 in terms of whole numbers, we would say the quotient is 0 (since we only consider whole number results).

**Conclusion:** This statement is **False (F)**.

### Statement II:
"Sum of two whole numbers is always less than their product."

**Analysis:**
- Let's take two whole numbers, for example, 2 and 3.
- Sum: \(2 + 3 = 5\)
- Product: \(2 \times 3 = 6\)
- Here, the sum (5) is less than the product (6).

- Now, let's take another example with 0 and 1:
- Sum: \(0 + 1 = 1\)
- Product: \(0 \times 1 = 0\)
- Here, the sum (1) is not less than the product (0).

**Conclusion:** This statement is **False (F)**.

### Statement III:
"Whole numbers are not closed under multiplication."

**Analysis:**
- Closure under an operation means that if you take any two whole numbers and perform the operation, the result should also be a whole number.
- For example, if we multiply 2 and 3:
\[ 2 \times 3 = 6 \]
6 is a whole number.
- If we take any two whole numbers, their product will always be a whole number.

**Conclusion:** This statement is **False (F)**.

### Final Answers:
- I: F
- II: F
- III: F