Results 1 to 2 of 2

Math Help - Proofs

  1. #1
    scottyflamingo
    Guest

    Proofs

    1.
    Prove: For all sets A and B, if A is a subset of B, then not B is a subset of not A.

    2.
    Prove: For all sets A,B,and C, A - (B U C) = (A-B) and (A-C)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    #1 is really only about logic. Recall that \left( {P \to Q} \right) \equiv \left( {\neg Q \to \neg P} \right).
    Thus If x is in A then x is in B. is equivalent to If xi is not in B then x is not in A.

    #2
    \begin{gathered}<br />
  A\backslash \left( {B \cup C} \right) \equiv A \cap \left( {B \cup C} \right)^c  \hfill \\<br />
   \equiv A \cap \left( {B^c  \cap C^c } \right) \hfill \\<br />
   \equiv \left( {A \cap B^c } \right) \cap \left( {A \cap C^c } \right) \hfill \\<br />
   \equiv \left( {A\backslash B} \right) \cap \left( {A \backslash C} \right) \hfill \\ <br />
\end{gathered}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. proofs
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: March 2nd 2010, 03:54 AM
  2. lim sup and lim inf proofs
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: February 24th 2010, 07:02 PM
  3. More Proofs
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: February 13th 2008, 07:05 PM
  4. Proofs
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 3rd 2008, 04:23 AM
  5. Replies: 3
    Last Post: October 6th 2007, 02:01 PM

Search Tags


/mathhelpforum @mathhelpforum