Question

which Venn diagram best describes the relationship among whole numbers, integers, rational numbers and natural numbers

Answer 1

To best describe the relationship among whole numbers, integers, rational numbers, and natural numbers using a Venn diagram, you can visualize it as follows:

1. **Natural Numbers (N)**: This set includes positive whole numbers (1, 2, 3, ...).
2. **Whole Numbers (W)**: This set includes all natural numbers plus zero (0, 1, 2, 3, ...).
3. **Integers (Z)**: This set includes all whole numbers and their negative counterparts (..., -3, -2, -1, 0, 1, 2, 3, ...).
4. **Rational Numbers (Q)**: This set includes all numbers that can be expressed as a fraction of two integers (including integers, since any integer can be expressed as a fraction by placing it over 1).

### Venn Diagram Structure:

1. **Rational Numbers (Q)** is the largest circle, as it encompasses all other sets, including integers, whole numbers, and natural numbers.
2. **Integers (Z)** is a circle inside the rational numbers. It overlaps with whole numbers and natural numbers.
3. **Whole Numbers (W)** is a circle inside the integers, containing all the non-negative integers (0, 1, 2, 3, ...).
4. **Natural Numbers (N)** is a smaller circle within the whole numbers, representing the positive integers (1, 2, 3, ...).

### Summary of Inclusion:
- Natural Numbers (N) ⊆ Whole Numbers (W) ⊆ Integers (Z) ⊆ Rational Numbers (Q).
- Whole Numbers (W) also contain zero, while Natural Numbers (N) do not.

In this arrangement, every set fits neatly within the one above it, clearly illustrating their relationships.