Results 1 to 2 of 2

Math Help - sets prove

  1. #1
    Senior Member
    Joined
    Jan 2009
    Posts
    381

    sets prove

    Show that for any sets A and B ,

    (A-B)U(B-A)=(AUB)-(AnB)


    thanks a lot ..
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,866
    Thanks
    745
    Hello, thereddevils!

    Show that for any sets A and B\!:\;\;<br />
(A-B) \cup (B-A) \:=\:(A \cup B)-(A \cap B)
    I'll establish some rules for reference:

    . . [1]\;\;P - Q \:=\:P \cap \overline{Q} . (definition of set subtraction)

    . . [2]\;P \cup \overline P \:=\:U

    . . [3]\;\;P \cap U \:=\:P



    \begin{array}{ccc}(A - B) \cup (B - A) & &\text{Given} \\ \\ (A \cap \overline B) \cup (B \cap \overline A) & & [1] \\ \\ \bigg[A \cup(B\cap \overline A)] \cap \bigg[\overline B \cup (B \cap \overline A)\bigg] & & \text{distr.} \\ \\ \bigg[(A \cup B) \cap (A \cup \overline A)\bigg] \cap \bigg[(\overline B \cup B) \cap (\overline B \cup \overline A)\bigg] & & \text{distr.} \\ \end{array}

    . . . \begin{array}{cccc} \bigg[(A \cup B) \cap U\bigg] \cap \bigg[U \cap (\overline B \cup \overline A)\bigg]\qquad && & [2] \\ \\ (A \cup B) \cap (\overline A \cup \overline B) & & & [3] \\ \\ (A \cup B) \cap (\overline{A \cap B}) & & & \text{DeMorgan} \\ \\ (A \cup B) - (A \cap B) & & & [1] \end{array}

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove the following equality of sets
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: July 30th 2010, 09:45 PM
  2. sets prove
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: June 3rd 2009, 02:58 PM
  3. sets prove
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: December 15th 2008, 08:55 AM
  4. Another sets prove
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: December 12th 2008, 07:28 AM
  5. prove equal sets
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 4th 2008, 09:27 AM

Search Tags


/mathhelpforum @mathhelpforum