anonymous
  • anonymous
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 = . @misty1212
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
and I can only choose one
misty1212
  • misty1212
is it closed under division? if you take a multiple of 5, and divide it by another multiple of 5, must the result be a multiple of 5? hint, what is \(20\div5\)?
anonymous
  • anonymous
20/5=4

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misty1212
  • misty1212
is 4 a multiple of 5?
anonymous
  • anonymous
no
anonymous
  • anonymous
at least I don't think so
misty1212
  • misty1212
right of course not
anonymous
  • anonymous
so it is not a?
misty1212
  • misty1212
so multiples of 5 are NOT closed under division \[20\div5=4\] is a "counterexample"
anonymous
  • anonymous
ok
misty1212
  • misty1212
definitely not A or B
anonymous
  • anonymous
oh and the answer to D. is 1/2
misty1212
  • misty1212
yes it is
anonymous
  • anonymous
so is the answer to the question D. or C.?
misty1212
  • misty1212
D
anonymous
  • anonymous
ok
misty1212
  • misty1212
\[25\div50=\frac{1}{2}\] is a "counter example"
misty1212
  • misty1212
since \(\frac{1}{2}\) is not a multiple of 5
anonymous
  • anonymous
can you explain why?
misty1212
  • misty1212
i say "all cats are gray" you show me a cat that is black and white that is a "counterexample" to my claim that all cats are gray, one cat that is not gray
anonymous
  • anonymous
oh ok
anonymous
  • anonymous
what I don't get is how 100/5=20 is not a counter example
misty1212
  • misty1212
because, dear, 20 IS a multiple of five i say all cats are gray, you show me a gray cat, that is not a counterexample
anonymous
  • anonymous
oh ok

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