Which statement is true about the relationships between the number sets?(1 point)
Responses
All integers are also rational numbers.
All integers are also rational numbers.
Not all natural numbers are real numbers.
Not all natural numbers are real numbers.
Some irrational numbers are also integers.
Not all natural numbers are real numbers.
I thought all numbers are real
You are correct, all numbers are real. I apologize for the mistake.
So what’s the answer
The correct answer 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, we can break down each statement and verify its accuracy.
Statement 1: All integers are also rational numbers.
To confirm this statement, we need to understand the definitions of integers and rational numbers.
Integers are whole numbers (including negative numbers) without fractional or decimal parts, such as -3, -2, -1, 0, 1, 2, 3, etc.
Rational numbers are numbers that can be expressed as a fraction or ratio of two integers, where the denominator is not zero. For example, 1/2, -3/4, 5/1, etc.
Since all integers can be expressed as a ratio of themselves divided by 1, they can also be written as fractions. Therefore, all integers are indeed rational numbers.
Statement 2: Not all natural numbers are real numbers.
To check the accuracy of this statement, we should understand the definitions of natural numbers and real numbers.
Natural numbers are counting numbers, including positive integers starting from 1, such as 1, 2, 3, 4, 5, etc.
Real numbers, on the other hand, include all rational and irrational numbers. Rational numbers are numbers that can be expressed as fractions, while irrational numbers cannot be expressed as fractions and often have endless, non-repeating decimal representations, such as √2 and π.
Since natural numbers are a subset of real numbers, it is correct to say that not all natural numbers are real numbers. For example, √2 and π are real numbers but not natural numbers.
Statement 3: Some irrational numbers are also integers.
To determine the validity of this statement, we need to understand the definitions of irrational numbers and integers.
Irrational numbers, as mentioned earlier, are numbers that cannot be expressed as fractions, often with decimal representations that go on indefinitely without repeating.
Integers, on the other hand, are whole numbers without fractional or decimal parts.
Since irrational numbers cannot be expressed as fractions, they cannot be written as integers. Therefore, it is incorrect to say that there are irrational numbers that are also integers.
In conclusion, the correct statement is "All integers are also rational numbers."