## ShadowCain one year ago For which operations is the set {–1, 0, 1} closed? Choose all answers that are correct. A. addition B. division C. multiplication D. subtraction

Division and Multiplication, right?

@zzr0ck3r @mathmate @King.Void. @SolomonZelman

3. blackstreet23

what does it mean set closed?

4. anonymous

A set 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.

5. anonymous

It's either A and D or all of them. I'm not sure

6. zzr0ck3r

ok let us go through them A) Is there a way to add two elements from the set and not get an element in the set?

Oh wait it can't be division because you can't divide by 0.....

8. zzr0ck3r

not addition because 1+1 = 2 is not in the set

yes -1 + 1 = 0

right?

11. jim_thompson5910

while `-1 + 1 = 0` is true, the fact that `1+1=2` means that you can take the elements `1` and `1` (repeat selections are possible), add them up, and get a number that is NOT in the set. So this set is NOT closed under addition

0 x -1 = 0 0 x 1 = 0 1 - 1 = 0 So, is it multiplication and subtraction?

13. jim_thompson5910

make a 3x3 table 3 rows for the elements -1,0,1 3 columns for the elements -1,0,1 |dw:1441669222547:dw|

14. jim_thompson5910

Now let's say we will use the subtraction operation to fill out the table, we subtract the value on the left from the value up top eg: -1 minus -1 = -1+1 = 0 and this goes in the first row, first column the rest of the table is filled out the same way |dw:1441669277363:dw|

15. jim_thompson5910

Does the table make sense?

So, it's only multiplication that will work?

17. jim_thompson5910

let's find out by making a multiplication table |dw:1441669432403:dw|

18. jim_thompson5910

so yes, the set is closed under multiplication take any two numbers (repeats allowed), multiply them, and you'll get some value that's in the set

19. jim_thompson5910

here's what the addition table would look like |dw:1441669534485:dw|

And division won't work either, right. Because you can't divide by 0

21. jim_thompson5910

correct

22. jim_thompson5910

division table |dw:1441669624730:dw|

Thanks for the help!!

24. jim_thompson5910

no problem