Which statement is true about the relationships between the number sets?
Some irrational numbers are also integers.
Not all natural numbers are real numbers.
Whole numbers include all natural numbers and 0.
All rational numbers are also integers.
Whole numbers include all natural numbers and 0.
The statement "Whole numbers include all natural numbers and 0" is true about the relationships between the number sets.
To determine which statement is true about the relationships between number sets, let's analyze each statement:
1. Some irrational numbers are also integers:
To verify this statement, we need to understand the definitions of irrational and integer numbers. Irrational numbers are those that cannot be expressed as a fraction or a ratio of two integers, such as √2 or π. On the other hand, integer numbers include both positive and negative whole numbers, as well as zero. Since there are no irrational numbers that can be integers (as they cannot be expressed as fractions), this statement is false.
2. Not all natural numbers are real numbers:
This statement is true. Natural numbers are the positive whole numbers (1, 2, 3, ...) which are a subset of the set of real numbers. Real numbers include not only the natural numbers but also numbers with decimal representations, fractions, and irrational numbers.
3. Whole numbers include all natural numbers and 0:
This statement is true. Whole numbers are the set of numbers that includes all of the natural numbers (positive whole numbers) along with the number zero (0).
4. All rational numbers are also integers:
To check the validity of this statement, we need to understand the definitions of rational and integer numbers. Rational numbers are numbers that can be expressed as a fraction or a ratio of two integers, such as 1/2 or -3/5. On the other hand, integer numbers include both positive and negative whole numbers, as well as zero. Since not all rational numbers are integers (e.g., √2/2 is rational but not an integer), this statement is false.
Therefore, the statement "Whole numbers include all natural numbers and 0" is true about the relationships between the number sets.