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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

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  1. ShadowCain
    • one year ago
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    Division and Multiplication, right?

  2. ShadowCain
    • one year ago
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    @zzr0ck3r @mathmate @King.Void. @SolomonZelman

  3. blackstreet23
    • one year ago
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    what does it mean set closed?

  4. anonymous
    • one year ago
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    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
    • one year ago
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    It's either A and D or all of them. I'm not sure

  6. zzr0ck3r
    • one year ago
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    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?

  7. ShadowCain
    • one year ago
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    Oh wait it can't be division because you can't divide by 0.....

  8. zzr0ck3r
    • one year ago
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    not addition because 1+1 = 2 is not in the set

  9. ShadowCain
    • one year ago
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    yes -1 + 1 = 0

  10. ShadowCain
    • one year ago
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    right?

  11. jim_thompson5910
    • one year ago
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    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

  12. ShadowCain
    • one year ago
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    0 x -1 = 0 0 x 1 = 0 1 - 1 = 0 So, is it multiplication and subtraction?

  13. jim_thompson5910
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    Does the table make sense?

  16. ShadowCain
    • one year ago
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    So, it's only multiplication that will work?

  17. jim_thompson5910
    • one year ago
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    let's find out by making a multiplication table |dw:1441669432403:dw|

  18. jim_thompson5910
    • one year ago
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    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
    • one year ago
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    here's what the addition table would look like |dw:1441669534485:dw|

  20. ShadowCain
    • one year ago
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    And division won't work either, right. Because you can't divide by 0

  21. jim_thompson5910
    • one year ago
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    correct

  22. jim_thompson5910
    • one year ago
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    division table |dw:1441669624730:dw|

  23. ShadowCain
    • one year ago
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    Thanks for the help!!

  24. jim_thompson5910
    • one year ago
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    no problem

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