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Math Help - Basic Set Theory Question

  1. #1
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    Basic Set Theory Question

    is |A| + |B| same as |A U B|?
    and why if they are not, i see that |AUB| is |A| + |B| - |A n B| (A intersect B)
    but why would you need to do that, cause if there are repeated elements then they can't repeat by them self cause sets are distinct elements...
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by AwesomeDesiKid View Post
    is |A| + |B| same as |A U B|?
    and why if they are not, i see that |AUB| is |A| + |B| - |A n B| (A intersect B)
    but why would you need to do that, cause if there are repeated elements then they can't repeat by them self cause sets are distinct elements...
    If A\cap B\ne\varnothing then \left|A\right|+\left|B\right| counts the repeated elements twice.
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  3. #3
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    Quote Originally Posted by Drexel28 View Post
    If A\cap B\ne\varnothing then \left|A\right|+\left|B\right| counts the repeated elements twice.
    well, i don't understand the difference between |A XOR B| and |A U B|
    xor is exclusive or(you probably know) wouldn't they equal the same thing
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by AwesomeDesiKid View Post
    well, i don't understand the difference between |A XOR B| and |A U B|
    xor is exclusive or(you probably know) wouldn't they equal the same thing
    My understanding is that A\text{ XOR }B=A\text{ }\Delta\text{ }B=\left(A-B\right)\cup\left(B-A\right). Is that correct?
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  5. #5
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    Quote Originally Posted by Drexel28 View Post
    My understanding is that A\text{ XOR }B=A\text{ }\Delta\text{ }B=\left(A-B\right)\cup\left(B-A\right). Is that correct?
    i have no idea what that delta means?
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  6. #6
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by AwesomeDesiKid View Post
    i have no idea what that delta means?
    Th symmetric difference. I told you want it means after that. In any case, I am moderately sure that I am correct in interpreting what you mean by A\text{ XOR }B. Your answer is then A\cup B=A\text{ XOR }B iff A\cap B=\varnothing.
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  7. #7
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    Quote Originally Posted by Drexel28 View Post
    Th symmetric difference. I told you want it means after that. In any case, I am moderately sure that I am correct in interpreting what you mean by A\text{ XOR }B. Your answer is then A\cup B=A\text{ XOR }B iff A\cap B=\varnothing.
    i think i got the difference, if |A U B| has all the elements from a and b.
    so if A = {0, 1, 2} and B = {1,2,3} then
    |A U B| = |0, 1, 2, 3} but
    |A XOR B| = {0. 3}
    if i m right....... thanks for the help, if not...I HAVE NO HOPE ANYMORE
    lol
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  8. #8
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by AwesomeDesiKid View Post
    i think i got the difference, if |A U B| has all the elements from a and b.
    so if A = {0, 1, 2} and B = {1,2,3} then
    |A U B| = |0, 1, 2, 3} but
    |A XOR B| = {0. 3}
    if i m right....... thanks for the help, if not...I HAVE NO HOPE ANYMORE
    lol
    ! One note though, \left|\text{some set}\right| usually means the cardinality.
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  9. #9
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    so A U B DOES equal A XOR B as long as A n B equals phi?
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