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Which statement is true about the relationships between the number sets?

Responses

Not all natural numbers are real numbers.
Not all natural numbers are real numbers. - no response given

All rational numbers are also integers.
All rational numbers are also integers. - no response given

Some irrational numbers are also integers.
Some irrational numbers are also integers. - no response given

Whole numbers include all natural numbers and 0.

1 answer

Let's analyze the statements one by one:

  1. Not all natural numbers are real numbers.

    • This statement is false. All natural numbers are indeed real numbers.

  2. All rational numbers are also integers.

    • This statement is false. While all integers are rational numbers (since they can be expressed as a fraction with a denominator of 1), not all rational numbers are integers (for example, 1/2 is a rational number but not an integer).

  3. Some irrational numbers are also integers.

    • This statement is false. By definition, irrational numbers cannot be expressed as fractions of integers, and therefore cannot be integers.

  4. Whole numbers include all natural numbers and 0.

    • This statement is true. Whole numbers are defined as the set of natural numbers (1, 2, 3, ...) along with 0.

Based on this analysis, the true statement is: Whole numbers include all natural numbers and 0.