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Basic set theory question about complement

  1. Jan 31, 2013 #1
    1. The problem statement, all variables and given/known data


    Hi I could use some help getting an explanation that kinda twists my head a bit.
    I want to know what I'm missunderstanding so I can get this right from the beginning.
    ^c = complement
    U = union

    I want to simplify this set
    A U (A U B^c)^c intersect (A U C )
    to
    AU(BnC)
    Using set theory laws

    3. The attempt at a solution


    So I start using set theory rules.

    De Morgans
    A U (A^c intersect B) intersect (A U C)

    Distributive Law
    A U (A^c intersect B) intersect C)

    This seem to be the same as AU(BnC), so it seems A^c doesn't have any impact.
    When using the distributive law can I do like this?
    A U ((B^c)^c intersect C)
    I would really appreciate any explanation on why this is and if there's any fault in my logic.
    Thanks
     
  2. jcsd
  3. Jan 31, 2013 #2
    you know that A^cB <=> A Intersect B barre*
    Relationships between relative and absolute complements:
    A ∖ B = A ∩ Bc (Bc is the elements out of the set b )
    *sorry we read math in french dunno how to explain it it's b with a line
    check this article on wikipedia http://en.wikipedia.org/wiki/Complement_(set_theory [Broken])
    at Relationships between relative and absolute complements:
     
    Last edited by a moderator: May 6, 2017
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