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.
The statement "Whole numbers include all natural numbers and 0" is true.
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 a whole number but not an integer.
It is a whole number but not an integer.
It is an integer but not a rational number.
It is an integer but not a rational number.
It is an integer but not a whole number.
The statement "It is both an integer and a whole number" is true about -9.
The statement that is true about the relationships between the number sets is: Whole numbers include all natural numbers and 0.
To determine which statement is true about the relationships between the number sets, we need to understand the definitions of each number set.
1. Natural numbers: These are the counting numbers, starting from 1 and going infinitely (1, 2, 3, 4...).
2. Integers: These include all the natural numbers (positive counting numbers), their negatives (negative counting numbers), and zero (-∞, ..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ...).
3. Rational numbers: These numbers can be expressed as a fraction of two integers (including integers themselves) and can be either terminating or recurring decimals.
4. Irrational numbers: These numbers cannot be expressed as a fraction of two integers and their decimal representation cannot be terminated or recurring (e.g., √2, π).
Now, let's analyze each statement:
Statement 1: "Some irrational numbers are also integers."
This statement is false. Irrational numbers, by definition, cannot be expressed as integers or fractions of two integers. For example, √2 or π cannot be written as whole numbers like 1, 2, 3, etc.
Statement 2: "Not all natural numbers are real numbers."
This statement is true. Natural numbers only include positive counting numbers, but real numbers include all rational numbers (fractions and integers) and irrational numbers. Therefore, not all natural numbers (which are positive integers) are real numbers.
Statement 3: "All rational numbers are also integers."
This statement is false. Rational numbers can be expressed as fractions of two integers, and these fractions can be integers (e.g., 1 = 1/1, 2 = 2/1), but not all rational numbers are integers. Examples of rational numbers that are not integers are 1/2, -3/4, or 5/7.
Statement 4: "Whole numbers include all natural numbers and 0."
This statement is true. Whole numbers include all the natural numbers and also include zero. So, the set of whole numbers would include 0, 1, 2, 3, 4, ...
Therefore, the correct answer is the last statement: "Whole numbers include all natural numbers and 0."