State 'T' for true of 'F' for false and select the correct option.
(i) Every natural number is a rational number.
(ii) Every rational number is a fraction.
(iii) Zero is not a retional number.
(iv) The reciprocal of 0 is `(1)/(0).`

Options

A. `{:(""(i), (ii), (iii), (iv)),(F, T, T, F):}`
B. `{:(""(i), (ii), (iii), (iv)),(T,T,T,F):}`
C. `{:(""(i), (ii), (iii), (iv)),(T,F,F,F):}`
D. `{:(""(i), (ii), (iii), (iv)),(T,T,F,F):}`

Answer

To solve the question, we need to evaluate each statement and determine whether it is true (T) or false (F).

### Step-by-Step Solution:

1. **Evaluate Statement (i)**: "Every natural number is a rational number."
- **Explanation**: Natural numbers are the set of positive integers (1, 2, 3, ...). A rational number is defined as any number that can be expressed in the form \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \). Each natural number can be expressed as a fraction with a denominator of 1 (e.g., 1 can be written as \( \frac{1}{1} \), 2 as \( \frac{2}{1} \), etc.).
- **Conclusion**: This statement is **True (T)**.

2. **Evaluate Statement (ii)**: "Every rational number is a fraction."
- **Explanation**: By definition, rational numbers can be expressed as fractions of integers. For example, \( \frac{3}{5} \), \( 0 \) (which can be written as \( \frac{0}{1} \)), and \( 2 \) (which can be written as \( \frac{2}{1} \)) are all examples of rational numbers expressed as fractions.
- **Conclusion**: This statement is **True (T)**.

3. **Evaluate Statement (iii)**: "Zero is not a rational number."
- **Explanation**: Zero can be expressed as a fraction, specifically \( \frac{0}{1} \). Since it can be expressed in the form \( \frac{p}{q} \) where \( p = 0 \) and \( q = 1 \) (with \( q \neq 0 \)), zero is indeed a rational number.
- **Conclusion**: This statement is **False (F)**.

4. **Evaluate Statement (iv)**: "The reciprocal of 0 is \( \frac{1}{0} \)."
- **Explanation**: The reciprocal of a number \( x \) is defined as \( \frac{1}{x} \). However, division by zero is undefined in mathematics. Therefore, the reciprocal of zero does not exist.
- **Conclusion**: This statement is **False (F)**.

### Final Answers:
- (i) T
- (ii) T
- (iii) F
- (iv) F

### Summary:
The correct options are:
- (i) True
- (ii) True
- (iii) False
- (iv) False