Which statement is true about the relationships between the number sets?
1) Some irrational numbers are also integers.
2) All rational numbers are also integers.
3) Not all natural numbers are real numbers.
4) Whole numbers include all natural numbers and 0.
The statement that is true about the relationships between the number sets is:
4) Whole numbers include all natural numbers and 0.
The correct statement about the relationships between the number sets is:
4) Whole numbers include all natural numbers and 0.
Explanation:
- Whole numbers include all natural numbers (1, 2, 3, ...)
- Whole numbers also include 0 (0)
- Natural numbers are a subset of whole numbers, meaning all natural numbers are also whole numbers.
- Irrational numbers are numbers that cannot be expressed as fractions. They include numbers like π (pi) and √2. They are not integers, which are whole numbers. So, statement 1 is false.
- Rational numbers are numbers that can be expressed as fractions. This includes integers as well. However, not all rational numbers are integers. For example, 3/2 is a rational number but not an integer. So, statement 2 is false.
- Real numbers include all rational and irrational numbers. Natural numbers are a subset of real numbers, as they are also rational numbers. Therefore, statement 3 is false.