Are the following statements true or false ? Give reasons for your answers.
(i) Every whole number is a natural number.
(ii) Every whole number is a rational number.
(iii) Every integer is a rational number.
(iv) Every rational number is a whole number.

Answer

Let's analyze each statement step by step and determine whether they are true or false, along with the reasoning for each answer.

### Statement Analysis:

**(i) Every whole number is a natural number.**

1. **Understanding Whole Numbers:** Whole numbers include 0, 1, 2, 3, and so on.
2. **Understanding Natural Numbers:** Natural numbers are the set of positive integers starting from 1 (i.e., 1, 2, 3, ...).
3. **Comparison:** Since whole numbers include 0 and natural numbers do not, not every whole number is a natural number.

**Conclusion:** This statement is **False**.
**Reason:** 0 is a whole number but not a natural number.

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**(ii) Every whole number is a rational number.**

1. **Understanding Rational Numbers:** Rational numbers are numbers that can be expressed as the quotient of two integers (a/b), where b ≠ 0.
2. **Whole Numbers as Rational Numbers:** Any whole number can be expressed as itself divided by 1 (e.g., 3 can be written as 3/1).
3. **Comparison:** Since every whole number can be expressed in the form of a rational number, this statement holds true.

**Conclusion:** This statement is **True**.
**Reason:** Every whole number can be expressed as a fraction (e.g., n/1), which fits the definition of a rational number.

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**(iii) Every integer is a rational number.**

1. **Understanding Integers:** Integers include positive numbers, negative numbers, and zero (i.e., ..., -3, -2, -1, 0, 1, 2, 3, ...).
2. **Integers as Rational Numbers:** Any integer can also be expressed as itself divided by 1 (e.g., -2 can be written as -2/1).
3. **Comparison:** Since every integer can be expressed in the form of a rational number, this statement is also true.

**Conclusion:** This statement is **True**.
**Reason:** Every integer can be expressed as a fraction (e.g., n/1), which fits the definition of a rational number.

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**(iv) Every rational number is a whole number.**

1. **Understanding Rational Numbers:** Rational numbers can be positive, negative, or zero and can be expressed as fractions (e.g., 1/2, -3/4).
2. **Whole Numbers as Rational Numbers:** Whole numbers are a subset of rational numbers but not all rational numbers are whole numbers.
3. **Comparison:** For example, 1/2 is a rational number but not a whole number.

**Conclusion:** This statement is **False**.
**Reason:** There are rational numbers (like 1/2) that are not whole numbers.

### Summary of Answers:
- (i) False - 0 is not a natural number.
- (ii) True - Whole numbers can be expressed as fractions.
- (iii) True - Integers can be expressed as fractions.
- (iv) False - Not all rational numbers are whole numbers.