Results 1 to 6 of 6

Math Help - Set Theory Help

  1. #1
    Newbie
    Joined
    Feb 2011
    Posts
    14

    Set Theory Help

    Hi,

    I'm currently going through past exams papers as part of my revision for my upcoming exams, however the past papers that I am using do not include answers, so I'm not sure if I'm on the right track or not.

    The question that I am working on is:

    Write down the letter corresponding to one true statement among the following:


    (A) {A,B}\{A,B,C}={A,B}
    (B) {A,B}\{A,B,C}={C}
    (C) {A,B}\{A,B,C}={A,B,C}
    (D) {A,B}\{A,B,C}={} (i.e. the empty set)
    (E) None of the above statements is true

    It has been a while since I did set theory as it was the beginning of the year and it was an area I struggled with, but am I right in saying that the correct answer is D?

    Any advice on this will be appreciated and if anybody can recommend any websites that contain example questions with answers, then this will be appreciated too.

    Follow Math Help Forum on Facebook and Google+

  2. #2
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello,

    Yes D is the correct answer !
    C\D = {elements of C that don't belong to D}
    Since C is included in D, there's no such element, hence the answer is the empty set !
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2011
    Posts
    14
    Quote Originally Posted by Moo View Post
    Hello,

    Yes D is the correct answer !
    C\D = {elements of C that don't belong to D}
    Since C is included in D, there's no such element, hence the answer is the empty set !
    Thanks for the response. I don't quite understand the second bit of your response, where you have mentioned that C is included in D and therefore there is no such element. Once I've got my head around this properly I think I'll be fine.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    C\D is the set of all elements of C not belonging to D.
    Buf if C is included in D, all the elements of C are in D (by definition of inclusion). Hence C\D=empty set
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,817
    Thanks
    316
    Awards
    1
    Quote Originally Posted by Gall1987 View Post
    Thanks for the response. I don't quite understand the second bit of your response, where you have mentioned that C is included in D and therefore there is no such element. Once I've got my head around this properly I think I'll be fine.
    Another way of looking at it. Think of the subtraction operation. (This is not a perfect analogy, but it works.)
    {A, B}\{A, B, C} = {A, B} - {A, B, C} <-- I've seen texts using this terminology, actually.

    A - A means A is removed.

    B - B means B is removed.

    -C means, well, don't do anything with C.

    What's left of {A, B}? Nothing. Both A and B have been removed. So {A, B}\{A, B, C} is the empty set.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1
    The defintion of X\setminus Y=X-Y\text{ is }X\cap Y^c.
    That is, X intersect Y complement.
    So nothing in Y can be in X\setminus Y.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Textbooks on Galois Theory and Algebraic Number Theory
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: July 8th 2011, 06:09 PM
  2. Set theory
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: July 13th 2009, 07:54 AM
  3. Group Theory - Sylow Theory and simple groups
    Posted in the Advanced Algebra Forum
    Replies: 16
    Last Post: May 16th 2009, 11:10 AM
  4. Problems relating Theory of Automata (Computer Theory)
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: October 17th 2007, 09:52 AM
  5. Set Theory
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 27th 2007, 09:22 AM

Search Tags


/mathhelpforum @mathhelpforum