Are the following statements true or false? Give reasons for your answer? Every whole number is a natural number Every integer is a rational number. Every rational number is an integer. Every natural number is a whole number. Every integer is a whole number Every rational number is a whole number

Explanation

Let's analyze each statement one by one and determine if they are true or false, providing reasons for each answer.

### Statement 1: Every whole number is a natural number.
**Answer:** False
**Reason:** Whole numbers include 0 (e.g., 0, 1, 2, 3, ...), while natural numbers start from 1 (e.g., 1, 2, 3, ...). Since 0 is a whole number but not a natural number, this statement is false.

### Statement 2: Every integer is a rational number.
**Answer:** True
**Reason:** Rational numbers are defined as numbers that can be expressed in the form of \( \frac{p}{q} \), where \( q \neq 0 \). Every integer can be expressed as a rational number by writing it as itself over 1 (e.g., \( 5 = \frac{5}{1} \), \( -3 = \frac{-3}{1} \)). Thus, this statement is true.

### Statement 3: Every rational number is an integer.
**Answer:** False
**Reason:** Rational numbers include fractions and decimals (e.g., \( \frac{1}{2}, -\frac{3}{4} \)), which are not integers. Therefore, not all rational numbers are integers, making this statement false.

### Statement 4: Every natural number is a whole number.
**Answer:** True
**Reason:** Natural numbers start from 1 and go up (1, 2, 3, ...), while whole numbers include 0 and all natural numbers (0, 1, 2, 3, ...). Thus, every natural number is indeed a whole number, making this statement true.

### Statement 5: Every integer is a whole number.
**Answer:** False
**Reason:** Integers include negative numbers (e.g., -1, -2, -3), while whole numbers are non-negative (0, 1, 2, ...). Since negative integers are not whole numbers, this statement is false.

### Statement 6: Every rational number is a whole number.
**Answer:** False
**Reason:** Rational numbers can be fractions or negative numbers (e.g., \( \frac{1}{2}, -\frac{3}{4} \)), which are not whole numbers. Therefore, this statement is false.

### Summary of Answers:
1. False
2. True
3. False
4. True
5. False
6. False