For which operation is the set of integers not closed?
A. addition
B. subtraction
C. multiplication
D. division**
I'm not sure on this one. Check my answer?
its division
division is the integer operation where the result is frequently NOT an integer
Uh, multiplication maybe? Since it's supposed to be the opposite of division.
sorry ... I was commenting on your CORRECT answer
Apologies, I read your original comment wrong..
so whats the answer?
To determine which operation the set of integers is not closed under, we need to understand what it means for a set to be closed under an operation.
A set is said to be closed under an operation if performing that operation on any two elements in the set yields a result that is still a member of the set.
Let's consider each operation:
A. Addition:
To check if the set of integers is closed under addition, we can take any two integers, add them together, and see if the result is still an integer. For example, if we take 2 and 3, the sum is 5, which is also an integer. So, the set of integers is closed under addition.
B. Subtraction:
To check if the set of integers is closed under subtraction, we can take any two integers, subtract one from the other, and see if the result is still an integer. For example, if we take 5 and 3, the difference is 2, which is also an integer. So, the set of integers is closed under subtraction.
C. Multiplication:
To check if the set of integers is closed under multiplication, we can take any two integers, multiply them together, and see if the result is still an integer. For example, if we take 4 and 6, the product is 24, which is still an integer. So, the set of integers is closed under multiplication.
D. Division:
To check if the set of integers is closed under division, we can take any two integers and divide one by the other, and see if the result is still an integer. For example, if we take 6 and 2, 6 divided by 2 equals 3, which is still an integer. However, if we take 6 and 4, 6 divided by 4 equals 1.5, which is not an integer. Therefore, the set of integers is not closed under division.
Based on this analysis, the correct answer is D. division.