Results 1 to 5 of 5

Math Help - Symmetric Difference

  1. #1
    Junior Member
    Joined
    Oct 2009
    Posts
    37

    Symmetric Difference

    I have a problem which s related to this symmetric propety.
    Show that there exist a unique set N such that (A \Delta N)=A for all A. The set N is obviously the empty set. But then how do I prove the uniqueness part of N, i.e. if (A \Delta N1)=A and (A \Delta N2)=A, then N1=N2= the empty set
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,957
    Thanks
    1780
    Awards
    1
    Quote Originally Posted by santiagos11 View Post
    I have a problem which s related to this symmetric propety.
    Show that there exist a unique set N such that (A \Delta N)=A for all A. The set N is obviously the empty set.
    A\Delta N = A\, \Rightarrow \,\left( {A\backslash N} \right) \cup (N\backslash A) = A\; \Rightarrow \;A \cap N^c  \subseteq A\;\& \;N \cap A^c  \subseteq A
    We know that N = \left( {N \cap A} \right) \cup \left( {N \cap A^c } \right).
    But that along with the above means that N \subseteq A. WHY?

    Now suppose that \left( {\exists p} \right)\left[ {p \in N} \right] this means that p \in N \cap A\; \Rightarrow \;p \notin N\backslash A \wedge p \notin A\backslash N.
    Is that a contradiction?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2009
    Posts
    37
    thank you. You are very good in your arguments.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Oct 2009
    Posts
    37
    I have yet another simmilar problem.
    Suppose A,B are sets. Show that there exist a unique set C such that (A \Delta C)=B. If A,B are disjoint, then C=A \cup B. But if not, then what would C have to be?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Oct 2009
    Posts
    37
    never mind. i got it
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Symmetric difference
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: January 25th 2011, 11:34 PM
  2. Symmetric Difference
    Posted in the Discrete Math Forum
    Replies: 9
    Last Post: November 3rd 2010, 09:49 AM
  3. Symmetric difference
    Posted in the Discrete Math Forum
    Replies: 10
    Last Post: June 7th 2010, 04:36 PM
  4. Symmetric Difference
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: September 5th 2009, 02:09 PM
  5. symmetric difference
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: January 27th 2009, 11:15 AM

Search Tags


/mathhelpforum @mathhelpforum