Kitten_is_back
  • Kitten_is_back
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 = .
Chemistry
katieb
  • katieb
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Photon336
  • Photon336
@Kitten_is_back start with the counter examples: do they disprove what's being said?
Kitten_is_back
  • Kitten_is_back
okay
Kitten_is_back
  • Kitten_is_back
d

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Kitten_is_back
  • Kitten_is_back
i got d ;-;
Photon336
  • Photon336
if (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
Kitten_is_back
  • Kitten_is_back
K
Photon336
  • Photon336
I 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. "
Kitten_is_back
  • Kitten_is_back
ph play
Kitten_is_back
  • Kitten_is_back
okay i mean
Photon336
  • Photon336
50/25 = 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
  • welshfella
d is correct 0.5 is not a multiple of 5
Kitten_is_back
  • Kitten_is_back
thanksd _^^

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