Results 1 to 3 of 3

Math Help - Symmetric Difference

  1. #1
    Newbie
    Joined
    Aug 2009
    Posts
    5

    Symmetric Difference

    The symmetric difference of A and B is
    (a) (A-B) \cap (B-A)
    (b) (A-B)\cup (B-A)
    (c) (A \cup B) - (A \cap B)
    (d) \{(A \cup B)-A\} \cup \{(A \cup B)-B\}

    Its answer given in the book is (b). But I found that (c) and (d) are also true. Am I right? If not please tell why. Thanks a lot for giving me your time.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570

    Symmetric Difference

    Hello ninni
    Quote Originally Posted by ninni View Post
    The symmetric difference of A and B is
    (a) (A-B) \cap (B-A)
    (b) (A-B)\cup (B-A)
    (c) (A \cup B) - (A \cap B)
    (d) \{(A \cup B)-A\} \cup \{(A \cup B)-B\}

    Its answer given in the book is (b). But I found that (c) and (d) are also true. Am I right? If not please tell why. Thanks a lot for giving me your time.
    You are right. (a) is the only expression not equal to the symmetric difference of the sets A and B.

    Grandad
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member Researcher's Avatar
    Joined
    Sep 2009
    Posts
    37
    Quote Originally Posted by ninni View Post
    The symmetric difference of A and B is
    (a) (A-B) \cap (B-A)
    (b) (A-B)\cup (B-A)
    (c) (A \cup B) - (A \cap B)
    (d) \{(A \cup B)-A\} \cup \{(A \cup B)-B\}

    Its answer given in the book is (b). But I found that (c) and (d) are also true. Am I right? If not please tell why. Thanks a lot for giving me your time.
    Yes you are right about (c).[I dindn'ttry to prove the others].
    One of the proofs of (c):
    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, 10:34 PM
  2. Symmetric Difference
    Posted in the Discrete Math Forum
    Replies: 9
    Last Post: November 3rd 2010, 08:49 AM
  3. Symmetric difference
    Posted in the Discrete Math Forum
    Replies: 10
    Last Post: June 7th 2010, 03:36 PM
  4. Symmetric Difference
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: November 30th 2009, 04:51 PM
  5. symmetric difference
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: January 27th 2009, 10:15 AM

Search Tags


/mathhelpforum @mathhelpforum