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Math Help - Proving DeMorgan Law?

  1. #1
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    Proving DeMorgan Law?

    Prove that (A \cup B)c = Ac \capBc (Demorganís Law)
    a)
    1) Let x be an arbitrary element of (A \cupB)c
    2) x \notin (A \cupB) (By Definition of Complement)
    3) x \notin A but x \in Ac (Definition of Union And Definition of Complement)
    4) x \notin B but x \in Bc (Definition of Union And Definition of Complement)

    5) x \in Ac, x \in Bc <-> x \inAc \capBc

    6) But x is an arbitrary element of (AUB)c

    7) Thus (A \cup B)c \subseteq Ac \capBc

    b) And Conversely
    1) Let y be an arbitrary element of Ac \cap Bc

    2) y \in Ac, y \in Bc (By Definition of intersection)

    3) y \notin A, y \notin B (Definition of Complement)

    4) y \notin A U B (From b(3))

    5) y \in (A U B)c

    6) But y is an arbitrary element of Ac \cap Bc

    7) Thus Ac \cap Bc \subseteq (A \cup B)c

    From a7 and b7 we have

    (A \cup B)c = Ac \cap Bc

    What is wrong in above statements? any help please?
    Thank You.

    Note: Solution is also atatched in doc file.
    Attached Files Attached Files
    Last edited by mrsenim; February 27th 2010 at 12:37 AM. Reason: Sorry I needed to post this
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