Which of the following properties holds for rational numbers and integers, but not for whole numbers?
A. Closure for addition
B. Closure for subtraction
C. Closure for multiplication
D. Closure for division
Which of the following properties holds for rational numbers and integers, but not for whole numbers?
A. Closure for addition
B. Closure for subtraction
C. Closure for multiplication
D. Closure for division
The closure property for addition and multiplication holds true for both rational numbers and integers. Division of rational numbers follows closure property (except 0),but the division of integers is not closed.
Now, the closure property of subtraction holds true for the rational numbers and integers. While, subtraction of whole numbers doesn’t follow the closure property, since the subtraction of any two whole numbers a and b, may or may not be a whole number.
As an example: 18−4=14 which is a whole number, but 4−18=−14 which is not a whole number.
Hence, the closure property of subtraction holds true for rational numbers and integers but it does not hold true for whole numbers.
Thus, (B) is the correct option.
The closure property for addition and multiplication holds true for both rational numbers and integers. Division of rational numbers follows closure property (except 0),but the division of integers is not closed.
Now, the closure property of subtraction holds true for the rational numbers and integers. While, subtraction of whole numbers doesn’t follow the closure property, since the subtraction of any two whole numbers a and b, may or may not be a whole number.
As an example: 18−4=14 which is a whole number, but 4−18=−14 which is not a whole number.
Hence, the closure property of subtraction holds true for rational numbers and integers but it does not hold true for whole numbers.
Thus, (B) is the correct option.
