ShadowCain
  • ShadowCain
For which operations is the set {–1, 0, 1} closed? Choose all answers that are correct. A. addition B. division C. multiplication D. subtraction
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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ShadowCain
  • ShadowCain
Division and Multiplication, right?
ShadowCain
  • ShadowCain
@zzr0ck3r @mathmate @King.Void. @SolomonZelman
blackstreet23
  • blackstreet23
what does it mean set closed?

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More answers

anonymous
  • 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.
anonymous
  • anonymous
It's either A and D or all of them. I'm not sure
zzr0ck3r
  • 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?
ShadowCain
  • ShadowCain
Oh wait it can't be division because you can't divide by 0.....
zzr0ck3r
  • zzr0ck3r
not addition because 1+1 = 2 is not in the set
ShadowCain
  • ShadowCain
yes -1 + 1 = 0
ShadowCain
  • ShadowCain
right?
jim_thompson5910
  • 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
ShadowCain
  • ShadowCain
0 x -1 = 0 0 x 1 = 0 1 - 1 = 0 So, is it multiplication and subtraction?
jim_thompson5910
  • 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|
jim_thompson5910
  • 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|
jim_thompson5910
  • jim_thompson5910
Does the table make sense?
ShadowCain
  • ShadowCain
So, it's only multiplication that will work?
jim_thompson5910
  • jim_thompson5910
let's find out by making a multiplication table |dw:1441669432403:dw|
jim_thompson5910
  • 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
jim_thompson5910
  • jim_thompson5910
here's what the addition table would look like |dw:1441669534485:dw|
ShadowCain
  • ShadowCain
And division won't work either, right. Because you can't divide by 0
jim_thompson5910
  • jim_thompson5910
correct
jim_thompson5910
  • jim_thompson5910
division table |dw:1441669624730:dw|
ShadowCain
  • ShadowCain
Thanks for the help!!
jim_thompson5910
  • jim_thompson5910
no problem

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