Which statement is true about the relationships between the number sets?(1 point)
Not all natural numbers are real numbers.
Whole numbers include all positive integers and negative integers.
Some irrational numbers are also integers.
All integers are also rational numbers.
Not all natural numbers are real numbers.
wrong
Apologies for the incorrect response. The true statement about the relationships between the number sets is:
All integers are also rational numbers.
The statement that is true about the relationships between the number sets is:
Not all natural numbers are real numbers.
To determine which statement is true about the relationships between the number sets, let's examine each statement individually:
Statement 1: Not all natural numbers are real numbers.
To assess this statement, we need to understand the definitions of natural numbers and real numbers. Natural numbers are the counting numbers, starting from 1 and progressing infinitely. Real numbers, on the other hand, encompass not only the natural numbers but also fractions, decimals, and irrational numbers. Therefore, statement 1 is true because real numbers include more than just natural numbers.
Statement 2: Whole numbers include all positive integers and negative integers.
To evaluate this statement, we need to understand the concept of whole numbers. Whole numbers consist of all the natural numbers (counting numbers) and zero. The positive integers are 1, 2, 3, and so on, while the negative integers are -1, -2, -3, and so forth. Since whole numbers include both positive and negative integers, statement 2 is true.
Statement 3: Some irrational numbers are also integers.
To assess this statement, we should remember that irrational numbers are the numbers that cannot be expressed as fractions and have non-repeating decimal representations. On the other hand, integers are whole numbers that include both positive and negative numbers, as well as zero. Therefore, since irrational numbers cannot be expressed as fractions, which are used to represent integers, statement 3 is false. Irrational numbers and integers are distinct number sets.
Statement 4: All integers are also rational numbers.
To evaluate this statement, we need to know the definition of rational numbers. Rational numbers can be expressed as the quotient of two integers, where the denominator is not zero. Integers can be expressed as the quotient of the number itself divided by one. Since any integer can be expressed as a fraction in this form, with a denominator of one, statement 4 is true. All integers are, indeed, rational numbers.
In summary, the true statements about the relationships between the number sets are:
- Not all natural numbers are real numbers.
- Whole numbers include all positive integers and negative integers.
- All integers are also rational numbers.