Let's analyze each statement by understanding the definitions of natural numbers, whole numbers, and integer numbers.

Understanding Number Types

• Natural Numbers ($\mathbb{N}$): These are the counting numbers. They start from 1 and go on infinitely. $\mathbb{N} = \{1, 2, 3, 4, ...\}$
• Whole Numbers ($\mathbb{W}$): These include all natural numbers plus zero. $\mathbb{W} = \{0, 1, 2, 3, 4, ...\}$
• Integers ($\mathbb{Z}$): These include all whole numbers and their negative counterparts. $\mathbb{Z} = \{..., -3, -2, -1, 0, 1, 2, 3, ...\}$

We can see a relationship between these sets:

Natural Numbers $\subset$ Whole Numbers $\subset$ Integers

This means that every natural number is a whole number, and every whole number is an integer. Consequently, every natural number is also an integer.

Evaluating Each Statement

Now let's check each statement given in the question:

1. Every natural number is a whole number.

   Natural numbers start from 1. Whole numbers include 0 and all natural numbers (1, 2, 3,...). Since every natural number is present in the set of whole numbers, this statement is true.

2. Every integer is a whole number.

   Integers include negative numbers (..., -3, -2, -1), zero (0), and positive numbers (1, 2, 3,...). Whole numbers include only zero (0) and positive numbers (1, 2, 3,...). Negative integers like -1, -2, etc., are integers but are not whole numbers. Therefore, this statement is not true.

3. Every natural number is an integer number.

   Natural numbers start from 1. Integers include all whole numbers (which include natural numbers) and negative numbers. Since every natural number (1, 2, 3,...) is present in the set of integers, this statement is true.

The question asks which statement is not true. Based on our evaluation, the statement "Every integer is a whole number" is the one that is not true.