Question

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

Answer 1

and I can only choose one

Answer 2

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 \(20\div5\)?

Answer 3

20/5=4

Answer 4

is 4 a multiple of 5?

Answer 5

no

Answer 6

at least I don't think so

Answer 7

right of course not

Answer 8

so it is not a?

Answer 9

so multiples of 5 are NOT closed under division \[20\div5=4\] is a "counterexample"

Answer 10

ok

Answer 11

definitely not A
or B

Answer 12

oh and the answer to D. is 1/2

Answer 13

yes it is

Answer 14

so is the answer to the question D. or C.?

Answer 15

D

Answer 16

ok

Answer 17

\[25\div50=\frac{1}{2}\] is a "counter example"

Answer 18

since \(\frac{1}{2}\) is not a multiple of 5

Answer 19

can you explain why?

Answer 20

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

Answer 21

oh ok

Answer 22

what I don't get is how 100/5=20 is not a counter example

Answer 23

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

Answer 24

oh ok