Which of the following statements are true and which are false?
(i) Every whole number is a rational number.
(ii) Every integer is a rational number.
(iii) 0 is a whole number but it is not a rational number.

Answer

To determine whether the statements are true or false, let's analyze each one step by step.

### Step 1: Analyze the first statement
**Statement (i): Every whole number is a rational number.**

- Whole numbers are defined as the set of numbers starting from 0 and going upwards: {0, 1, 2, 3, ...}.
- Rational numbers are defined as numbers that can be expressed in the form of \( \frac{P}{Q} \), where \( P \) and \( Q \) are integers and \( Q \neq 0 \).
- Any whole number \( n \) can be expressed as \( \frac{n}{1} \), which fits the definition of a rational number.

**Conclusion for Statement (i): True.**

### Step 2: Analyze the second statement
**Statement (ii): Every integer is a rational number.**

- Integers include all whole numbers and their negative counterparts: {..., -3, -2, -1, 0, 1, 2, 3, ...}.
- Similar to whole numbers, any integer \( n \) can also be expressed in the form \( \frac{n}{1} \).
- Therefore, every integer can be represented as a rational number.

**Conclusion for Statement (ii): True.**

### Step 3: Analyze the third statement
**Statement (iii): 0 is a whole number but it is not a rational number.**

- As established, 0 is indeed a whole number.
- Furthermore, 0 can be expressed as \( \frac{0}{1} \), which is in the form of \( \frac{P}{Q} \) where \( P = 0 \) and \( Q = 1 \).
- Therefore, 0 is also a rational number.

**Conclusion for Statement (iii): False.**

### Final Summary
- Statement (i): True
- Statement (ii): True
- Statement (iii): False

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