Which Venn diagram best represents the relationship among whole numbers, integers rational numbers, and natural numbers?

A. |Natural Numbers|
|Whole numbers|
|Rational Numbers|
|Integers|.
B. |Rational Numbers|
|Integers|
|Whole Numbers|
|Natural Numbers|.
C. |Integers|
|Rational Numbers|
|Natural Numbers|
|Whole Numbers|.
D. |Integers|
|Rational Numbers|
|Whole numbers|
|Natural Numbers|.

1 answer

To represent the relationship among whole numbers, integers, rational numbers, and natural numbers in a Venn diagram, we first need to understand the definitions of each set:

  1. Natural Numbers: These are the counting numbers starting from 1 (1, 2, 3, ...).
  2. Whole Numbers: These include all natural numbers along with 0 (0, 1, 2, 3, ...).
  3. Integers: This set includes all whole numbers and their negatives (..., -3, -2, -1, 0, 1, 2, 3, ...).
  4. Rational Numbers: These include all integers, as well as fractions and decimals that can be expressed as a ratio of two integers (e.g., 1/2, -3/4, 0.75, etc.).

Based on these definitions, we can visualize the relationships as follows:

  • Natural numbers are a subset of whole numbers.
  • Whole numbers are a subset of integers.
  • Integers are a subset of rational numbers.

Given the options:

A. |Natural Numbers| |Whole Numbers| |Rational Numbers| |Integers|.

  • This option places natural numbers separately, which is incorrect.

B. |Rational Numbers| |Integers| |Whole Numbers| |Natural Numbers|.

  • This option also places all together but doesn't show the correct subset relationships.

C. |Integers| |Rational Numbers| |Natural Numbers| |Whole Numbers|.

  • This option shows integers and rational numbers but misplaced natural and whole numbers.

D. |Integers| |Rational Numbers| |Whole numbers| |Natural Numbers|.

  • This option places natural numbers inside whole numbers, whole numbers inside integers, and integers within rational numbers. It correctly represents all the relationships.

Therefore, the best Venn diagram representation is:

D. |Integers| |Rational Numbers| |Whole numbers| |Natural Numbers|.