Question

Is the set of numbers that can be written as the product of 6 and an integer closed under subtraction?

A.
Yes, because the difference of any two multiples of 6 is equal to 6.

B.
Yes, because the difference of any two multiples of 6 is also a multiple of 6.

C.
No, and a counterexample is 6 – 6 = 0.

D.
No, and a counterexample is 6 – 18 = –12.

Answer 1

@TheEdwardsFamily @Directrix

Answer 2

help me please

Answer 3

We need to get an understanding of what these number look like.

>Is the set of numbers that can be written as the product of 6 and an integer closed


The integers are {...-3, -2, -1. 0, 1, 2, 3, ...}

Answer 4

6 times each of those would be:

{..., -18, -12, -6, 0, 6, 12, 18, ...}

Answer 5

yes...

Answer 6

The question is: if you pick any two of those numbers and subtract them, will you get an answer that is also in that set.

Answer 7

uhm. like..... 6-6=0?

Answer 8

Yes, because the difference of any two multiples of 6 is equal to 6.

12 is a multiple of 6
24 is a multiple of 6.

12 - 24 is not equal to 6. So, thrown out option A. It is wrong.

Answer 9

ok

Answer 10

C. No, and a counterexample is 6 – 6 = 0.

6 - 6 = 0 which is a multiple of 6 because 0 times 6 = 0.

So, throw out option C.

Answer 11

ok

Answer 12

So, which answer do you think is correct?

Answer 13

b?

Answer 14

i think....wait. no....D

Answer 15

Let's see: No, and a counterexample is 6 – 18 = –12.

6 - 18 = -12 but -12 is a multiple of 6 because 6 times -2 = -12.

Throw out option D.

Answer 16

What is left of the options to be the correct one. The option we have not yet investigated.

Answer 17

B

Answer 18

B. Yes, because the difference of any two multiples of 6 is also a multiple of 6.

Correct Answer.

Answer 19

OK.... THASNK YOU SOOO MUCH!!!!

Answer 20

You are welcome.