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Math Help - Question about Sets and Logic

  1. #1
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    Smile Question about Sets and Logic

    List the elements of each set. Show all your work.
    A = {1,2,5,6}
    B = {2,5,7}
    C= {1,3,5,7,9}
    A ⊕ B and A ⊕ C
    I am assuming the answer is {1,6,7} for A ⊕ B and {2,3,6,7,9} for A ⊕ C

    Which includes everything that is not intersected.

    Is this correct?
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  2. #2
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    You are correct.
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  3. #3
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    Is it ok to explain (A ⊕ B) as:

    (A ⊕ B) = { x | x ∈ A ⊕ x ∈ B}
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  4. #4
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    Quote Originally Posted by robasc View Post
    Is it ok to explain (A ⊕ B) as:

    (A ⊕ B) = { x | x ∈ A ⊕ x ∈ B}
    No it is not.
    A \oplus B = \left( {A \cup B} \right)\backslash \left( {A \cap B} \right) = \left( {A\backslash B} \right) \cup \left( {B\backslash A} \right)

    That is called symmetric difference.
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  5. #5
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    Is this the only one? Could I do this:

    (A ∪ C) - B = {x | x ∈ (A ∪ C) or x ∉ B)
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  6. #6
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    Quote Originally Posted by robasc View Post
    Is this the only one? Could I do this:
    (A ∪ C) - B = {x | x ∈ (A ∪ C) or x ∉ B)
    I have no idea what in the world you are trying to do.
    But it is (A ∪ C) - B = {x | x ∈ (A ∪ C) and x ∉ B)
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