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.
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.
To determine which statement is true about the relationships between the number sets, let's examine each option:
1. Some irrational numbers are also integers: This statement is not true. Irrational numbers are numbers that cannot be expressed as a fraction and have an infinite number of decimal places without repeating. Examples of irrational numbers include √2 and π. Integers, on the other hand, are whole numbers (negative, zero, and positive) without any decimal or fractional parts. Since irrational numbers cannot be expressed as integers, this statement is false.
2. All rational numbers are also integers: This statement is also false. Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are integers. Examples of rational numbers include 1/2, -3/4, and 7. Integers include both positive and negative whole numbers, but rational numbers can also be fractional. Therefore, not all rational numbers are integers.
3. Not all natural numbers are real numbers: This statement is true. Natural numbers are the counting numbers: 1, 2, 3, 4, and so on. Real numbers, on the other hand, include all the possible numbers on the number line, including natural numbers, rational numbers, irrational numbers, and integers. Therefore, there are more real numbers than just the natural numbers, making this statement true.
4. Whole numbers include all natural numbers and 0: This statement is true. Whole numbers consist of all the natural numbers (counting numbers) along with zero. Examples of whole numbers are 0, 1, 2, 3, and so on.
In summary, out of the given options, the statement that is true about the relationships between the number sets is: Whole numbers include all natural numbers and 0 (Option 4).