Which statement is true about the relationships between the number sets?(1 point)
A. Not all natural numbers are real numbers.
B. Whole numbers include all natural numbers and 0.
C.Some irrational numbers are also integers.
D.All rational numbers are also integers
Which of the following is true about −9?(1 point)
A.It is both an integer and a whole number.
B. It is a whole number but not an integer.
C.It is an integer but not a whole number.
D. It is an integer but not a rational number.
A. Not all natural numbers are real numbers.
C. It is an integer but not a whole number.
For the first question, the correct statement is options B. Whole numbers include all natural numbers and 0.
For the second question, the correct option is C. It is an integer but not a whole number.
To answer the first question, let's break down the options:
A. Not all natural numbers are real numbers.
This statement is true. Natural numbers only include positive whole numbers (1, 2, 3, ...) and do not include any fractions or decimals. Real numbers, on the other hand, include all rational and irrational numbers.
B. Whole numbers include all natural numbers and 0.
This statement is true. Whole numbers include all natural numbers (0, 1, 2, 3, ...) and also include 0.
C. Some irrational numbers are also integers.
This statement is false. Integers are whole numbers and their negatives (..., -3, -2, -1, 0, 1, 2, 3, ...). Irrational numbers cannot be written as fractions and do not have repeating or terminating decimals, so they cannot be integers.
D. All rational numbers are also integers.
This statement is false. Rational numbers are numbers that can be written as fractions, where the numerator and denominator are integers. Integers are a subset of rational numbers, but not all rational numbers are integers.
To answer the second question, let's analyze the options:
A. It is both an integer and a whole number.
This statement is incorrect. "-9" is an integer because it is a negative whole number, but it is not a whole number because it is negative. Whole numbers are non-negative, including zero.
B. It is a whole number but not an integer.
This statement is incorrect. As explained above, "-9" is an integer because it is a negative whole number, but it is not a whole number because it is negative.
C. It is an integer but not a whole number.
This statement is correct. "-9" is an integer because it is a negative whole number, but it is not a whole number because it is negative.
D. It is an integer but not a rational number.
This statement is incorrect. "-9" is an integer because it can be written as -9/1, where the numerator and denominator are integers. Therefore, it is also a rational number.