Which statement is true about the relationship between the number sets?
whole numbers include all natural numbers and 0
not all natural numbers are real numbers
some irrational numbers are also integers
all rational numbers are also integers
The statement that is true about the relationship between the number sets is:
Whole numbers include all natural numbers and 0.
The statement that is true about the relationship between the number sets is: "Whole numbers include all natural numbers and 0."
Explanation:
- Whole numbers include all natural numbers (positive integers) and the number 0.
- Not all natural numbers are real numbers. Natural numbers are a subset of real numbers, but real numbers also include irrational and rational numbers.
- Some irrational numbers can also be integers, but not all of them. For example, the square root of 9 is an irrational number (3), but it is also an integer.
- All rational numbers are not integers. Rational numbers include integers, but they also include fractions (such as 1/2 or -3/4), which are not integers.
To determine which statement is true about the relationship between the number sets, let's analyze each statement individually:
1. "Whole numbers include all natural numbers and 0": This statement is true. Whole numbers are the set of positive integers (natural numbers) including zero (0). So, the whole numbers consist of all the natural numbers plus the number 0.
2. "Not all natural numbers are real numbers": This statement is false. Natural numbers are a subset of real numbers. Real numbers consist of all rational and irrational numbers, including the natural numbers.
3. "Some irrational numbers are also integers": This statement is false. Irrational numbers are numbers that cannot be expressed as a fraction or a ratio of two integers. Integers, on the other hand, include both positive and negative whole numbers. Since irrational numbers cannot be represented as integers, this statement is not true.
4. "All rational numbers are also integers": This statement is false. Rational numbers are numbers that can be expressed as a fraction or a ratio of two integers. However, not all rational numbers are integers. Integers include both positive and negative whole numbers, whereas rational numbers can also include proper fractions and mixed numbers.
In conclusion, the true statement about the relationship between the number sets is that "whole numbers include all natural numbers and 0."