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Kitten_is_back
 one year ago
Is the set of multiples of 5 closed under division? Explain why or provide a counterexample if not.
A.
Yes, because the quotient of any two multiples of 5 is also a multiple of 5.
B.
Yes, because the quotient of any two multiples of 5 is also a multiple of 10.
C.
No, and a counterexample is 100 ÷ 5 = 20.
D.
No, and a counterexample is 25 ÷ 50 = .
Kitten_is_back
 one year ago
Is the set of multiples of 5 closed under division? Explain why or provide a counterexample if not. A. Yes, because the quotient of any two multiples of 5 is also a multiple of 5. B. Yes, because the quotient of any two multiples of 5 is also a multiple of 10. C. No, and a counterexample is 100 ÷ 5 = 20. D. No, and a counterexample is 25 ÷ 50 = .

This Question is Closed

Photon336
 one year ago
Best ResponseYou've already chosen the best response.0@Kitten_is_back start with the counter examples: do they disprove what's being said?

Photon336
 one year ago
Best ResponseYou've already chosen the best response.0if (a/b), (b/a), a,b belong to the set than it has to be closed I think. a/b,b/a ,a,b belong to the given set then it is closed. let me see

Photon336
 one year ago
Best ResponseYou've already chosen the best response.0I found a great explanation to this hopefully it helps you "A group of elements is closed under an operation if, when you apply the operation to elements of the set, you always get another element of the set. Like whole numbers are closed under addition, because if you add two whole numbers, you always get another whole number  there is no way to get anything else. But the whole numbers are _not_ closed under subtraction, because you can subtract two whole numbers to get something that is not a whole number, e.g., 2  5 = 3 The integers are closed under multiplication (if you multiply two integers, you get another integer), but they are _not_ closed under division, since you can divide two integers to get a rational number that isn't an integer. The rationals, however, are closed under addition, subtraction, multiplication, and division. "

Photon336
 one year ago
Best ResponseYou've already chosen the best response.050/25 = 2 but 25/50 = 0.5 which isn't an integer. I think this might be the answer because both are multiples of 5 and they aren't closed under division.I think you should always get a multiple of 5. I think you're correct it's D.

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0d is correct 0.5 is not a multiple of 5
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