Which statement is true about the relationships between the number sets?(1 point)
Responses
Some irrational numbers are also integers.
Some irrational numbers are also integers.
Whole numbers include all natural numbers and 0.
Whole numbers include all natural numbers and 0.
All rational numbers are also integers.
All rational numbers are also integers.
Not all natural numbers are real numbers.
Not all natural numbers are real numbers.
Which of the following is true about −9?(1 point)
Responses
It is both an integer and a whole number.
It is both an integer and a whole number.
It is an integer but not a whole number.
It is an integer but not a whole number.
It is an integer but not a rational number.
It is an integer but not a rational number.
It is a whole number but not an integer.
The statement "Not all natural numbers are real numbers" is true.
To determine which statement is true about the relationships between the number sets, we need to understand the definitions and relationships between these number sets.
1. Some irrational numbers are also integers: Irrational numbers are numbers that cannot be expressed as a fraction or ratio of two integers. Examples include √2, π, and e. Integers, on the other hand, are whole numbers that can be positive, negative, or zero. Examples include -3, 0, and 5. Since irrational numbers cannot be expressed as a fraction, they cannot be integers. Therefore, the statement "Some irrational numbers are also integers" is false.
2. Whole numbers include all natural numbers and 0: Natural numbers, also known as counting numbers, are the positive integers starting from 1. Whole numbers are the natural numbers including 0. Therefore, the statement "Whole numbers include all natural numbers and 0" is true.
3. All rational numbers are also integers: Rational numbers are numbers that can be expressed as a fraction or ratio of two integers. Examples include 1/2, -3/4, and 5/1. Integers are whole numbers that can be positive, negative, or zero. Since all integers can be expressed as a fraction (e.g., 5/1 or -3/1), all integers are also rational numbers. Therefore, the statement "All rational numbers are also integers" is true.
4. Not all natural numbers are real numbers: Real numbers include all rational and irrational numbers. Natural numbers are a subset of real numbers, but not all real numbers are natural numbers. Irrational numbers, as mentioned earlier, cannot be expressed as a fraction or ratio of two integers. Therefore, the statement "Not all natural numbers are real numbers" is true.
In conclusion, the statement "Whole numbers include all natural numbers and 0" is true, and the statements "Some irrational numbers are also integers" and "All rational numbers are also integers" are false. The statement "Not all natural numbers are real numbers" is true.