Results 1 to 3 of 3

Math Help - More basic topology (couple questions)

  1. #1
    Junior Member
    Joined
    Nov 2009
    Posts
    64

    More basic topology (couple questions)

    1) I have to prove: (A \cup B) - (A \cap B) = (A-B) \cup (B-A)

    I know some people get annoyed by the "-" notation, but that is what my prof uses, so...

    Here is my work:

    (A \cup B) - (A \cap B) = (A \cup B) \cap (A \cap B)^c

    =(A \cup B) \cap (A^c \cup B^c)

    =(A \cup B) \cup (B \cap A^c)

    =(A-B) \cup (B-A)


    2) Let X = \{ a,b,c,d \}

    and let S = \{ \O , \{ a,b \} , \{ b,c \} , \{ c,d \} , \{  a,d \} , \{ a,b,c,d \} \}

    I have to find the smallest topology on X that contains S.

    So, using the axioms for a topological space:

    \{ \{ S, \{ a \} , \{ b \} , \{ c \} , \{ d \} , \{ b,d \} , \{ a,c \} , \{ a,b,c \} , \{ a,b,d \} , \{ b,c,d \} , \{ a,c,d \} \}

    Correct?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,649
    Thanks
    1597
    Awards
    1
    You missed an important equality.
    (A \cup B) \cap (A^c \cup B^c)=(A\cap B^c)\cup(B\cap A^c).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2009
    Posts
    64
    Oh right, so it should have been:

    (A \cup B) - (A \cap B) = (A \cup B) \cap (A \cap B)^c

    =(A \cup B) \cap (A^c \cup B^c)

    =(A \cap B^c) \cup (B \cap A^c)

    =(A-B) \cup (B-A)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help on a couple basic Trig Questions
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: January 21st 2011, 06:45 PM
  2. A couple of basic calculus problems
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 23rd 2010, 04:16 AM
  3. Basic Topology
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: January 2nd 2010, 09:20 PM
  4. help me solve some basic topology questions for fast CASH!!!
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: November 8th 2009, 04:53 PM
  5. Couple of basic chemistry questions
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: June 5th 2007, 04:03 PM

Search Tags


/mathhelpforum @mathhelpforum