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.
Not all natural numbers are real numbers.
Not all natural numbers are real numbers.
All rational numbers are also integers.
All rational numbers are also integers.
Whole numbers include all natural numbers and 0.
Whole numbers include all natural numbers and 0.
Which of the following is true about −9?(1 point)
Responses
It is an integer but not a whole number.
It is an integer but not a whole number.
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 rational number.
It is an integer but not a rational number.
It is a whole number but not an integer.
The statement "Whole numbers include all natural numbers and 0" is true.
To determine which statement is true about the relationships between the number sets, we need to understand the definitions of each number set.
1. Irrational numbers: These are numbers that cannot be expressed as a fraction or ratio of two integers. Examples include √2 and π.
2. Integers: These are the set of whole numbers (positive, negative, or zero) and their opposites. Examples include -3, 0, and 5.
3. Natural numbers: These are the positive integers (excluding zero). Examples include 1, 2, and 3.
4. Real numbers: These include all rational and irrational numbers.
Now, let's evaluate each statement:
Statement 1: Some irrational numbers are also integers.
Explanation: This statement is false. Irrational numbers cannot be expressed as integers. For example, √2 is an irrational number, but it cannot be written as a whole number like 2 or -2.
Statement 2: Not all natural numbers are real numbers.
Explanation: This statement is true. Natural numbers are a subset of real numbers, but not all real numbers are natural numbers. Real numbers include both rational and irrational numbers, so there are real numbers that are not natural numbers. For example, π is a real number but not a natural number.
Statement 3: All rational numbers are also integers.
Explanation: This statement is false. Rational numbers can be expressed as a fraction or ratio of two integers, but they are not limited to integers. For example, 1/2 is a rational number, but it is not an integer.
Statement 4: Whole numbers include all natural numbers and 0.
Explanation: This statement is true. Whole numbers consist of all natural numbers (positive integers) including zero. For example, 0, 1, 2, 3, etc., are all whole numbers.
In conclusion, the correct statement about the relationships between the number sets is: Whole numbers include all natural numbers and 0.