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Math Help - Set logic proof question

  1. #1
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    Set logic proof question

    Prove: if F = a U b and a intersect b = disjoint, then a = F\b.

    sorry I didnt know the latex for some of these things.

    doesnt this mean that a is a subset of F and not in b?

    i think i know how to prove that a is a subset of F\b but how do I prove that F\b is a subset of a?
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  2. #2
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    Quote Originally Posted by p00ndawg View Post
    Prove: if F = a U b and a intersect b = disjoint, then a = F\b.
    sorry I didnt know the latex for some of these things.
    doesnt this mean that a is a subset of F and not in b?
    i think i know how to prove that a is a subset of F\b but how do I prove that F\b is a subset of a?
    [tex] F=A\cup B [/tex] gives F=A \cup B
    [tex]A\cap B= \emptyset [/tex] gives A\cap B= \emptyset .
    [tex] A = F\setminus B [/tex] gives  A = F\setminus B .

    Proof.
    If  x\in A then because  F=A\cup B ~\&~ A\cap B= \emptyset then what?
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  3. #3
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    Quote Originally Posted by Plato View Post
    [tex] F=A\cup B [/tex] gives F=A \cup B
    [tex]A\cap B= \emptyset [/tex] gives A\cap B= \emptyset .
    [tex] A = F\setminus B [/tex] gives  A = F\setminus B .

    Proof.
    If  x\in A then because  F=A\cup B ~\&~ A\cap B= \emptyset then what?

    A is a subset of F\setminus B?
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  4. #4
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    Quote Originally Posted by p00ndawg View Post
    A is a subset of F\setminus B? YES
    If x\in F\setminus B then does x\in A? WHY?
    What does that tell us?
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  5. #5
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    Quote Originally Posted by Plato View Post
    If x\in F\setminus B then does x\in A? WHY?
    What does that tell us?
    X has to be in F because it is not in B, and since A is a subset of F\B we know that A has to be in F.

    that right?
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  6. #6
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    Quote Originally Posted by p00ndawg View Post
    X has to be in F because it is not in B, and since A is a subset of F\B we know that A has to be in F. that right?
    YES
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