Let's evaluate each statement regarding the relationships between the number sets:
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Whole numbers include all natural numbers and 0.
- This statement is true. Whole numbers are defined as all natural numbers (1, 2, 3, ...) plus zero.
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Not all natural numbers are real numbers.
- This statement is false. Natural numbers (1, 2, 3, ...) are a subset of real numbers, so all natural numbers are indeed real numbers.
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All rational numbers are also integers.
- This statement is false. Rational numbers include integers (like -1, 0, 1, 2), as well as fractions (like 1/2, 3/4), so not all rational numbers are integers.
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Some irrational numbers are also integers.
- This statement is false. By definition, irrational numbers cannot be expressed as a fraction of two integers, while integers are whole numbers (positive, negative, or zero). Therefore, no irrational number can be an integer.
In conclusion, the only true statement is:
- Whole numbers include all natural numbers and 0.