Results 1 to 2 of 2

Thread: Proof involving sets

  1. #1
    Junior Member
    Joined
    Sep 2008
    From
    Oregon
    Posts
    58

    Exclamation Proof involving sets

    X \ ( A ^ B ) = ( X \ A ) U ( X \ B )

    I know I have to show (prove) containment in both directions to prove equality...but I'm not sure even where to start with this.

    Thanx in advance for the help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    20,281
    Thanks
    2217
    Awards
    1
    It is easy.
    \begin{array}{rcl}<br />
   {X\backslash \left( {A \cap B} \right)} &  \Leftrightarrow  & {X \cap \left( {A \cap B} \right)^c }  \\<br />
   {} &  \Leftrightarrow  & {X \cap \left( {A^c  \cup B^c } \right)}  \\<br />
   {} &  \Leftrightarrow  & {\left( {X \cap A^c } \right) \cup \left( {X \cap B^c } \right)}  \\<br />
   {} &  \Leftrightarrow  & {\left( {X\backslash A} \right) \cup \left( {X\backslash B} \right)}  \\<br /> <br />
 \end{array}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. proof involving power sets, and intersection
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: Jan 12th 2010, 02:29 PM
  2. proof involving differences of sets
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Oct 13th 2009, 03:36 PM
  3. Try these proofs involving sets
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: Apr 15th 2009, 02:29 AM
  4. Proofs involving sets and their compliments
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Apr 14th 2009, 11:06 PM
  5. Replies: 2
    Last Post: Oct 4th 2008, 04:57 PM

Search Tags


/mathhelpforum @mathhelpforum