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    Set Theory: Set Operations

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    Bridge to Abstract Mathematics
    Set Theory: Set Operations

    Let A, B, C and D be sets. Prove that....
    a) A B iff A B = Ø.
    b) If A B U C and A ∩ B = Ø, then A C.
    c) C A ∩ B iff C A and C B.
    d) If A B, then A C B C.
    e) (A B) C = (A C) (B C).
    f) If A C and B C, then A U B C.
    g) (A U B ) ∩ C A U (B ∩ C).
    h) A B and B are disjoint.
    i) If C A and D B, then C ∩ D A ∩ B.
    j) If C A and D B, then C U D A U B.
    k) If C A, D B, and A and B are disjoint, then C and D are disjoint.
    l) If C A and D B, then D A B C.
    m) If A U B C U D, A ∩ B = Ø, and C A, then B D.

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    Solution Preview

    a) If , then , thus .
    If , then , thus .
    b) If , and , then , thus .
    c) If , then and , then and ; if and , then , thus .
    d) If , then ...

    Solution Summary

    Provide an example of each type of proof attached.