Results 1 to 2 of 2

Math Help - Power Sets

  1. #1
    Member
    Joined
    Sep 2008
    Posts
    81

    Power Sets

    I have a question here that says:

    Let A = {1,2,3,4,5,6} and let S = P(A), the power set of A.

    a) For a,b belong to S, define a ~ b if a and b have the same number of elements. Prove that ~ defines an equivalence relation on S.

    b) How many equivalence classes are there? List one element from each equivalence class.

    Could someone steer me in the right direction? Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,658
    Thanks
    1615
    Awards
    1
    Quote Originally Posted by GreenDay14 View Post
    I have a question here that says:
    Let A = {1,2,3,4,5,6} and let S = P(A), the power set of A.
    a) For a,b belong to S, define a ~ b if a and b have the same number of elements. Prove that ~ defines an equivalence relation on S.

    b) How many equivalence classes are there? List one element from each equivalence class.
    If from six we choose two, that can be done 15 ways.
    So the are 15 two element subsets. Hence equivalence class of two element subsets has 15 members.

    There are 7 different equivalence classes, one has only one element.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Cardinality of Sets and Power Sets
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: September 8th 2011, 05:26 PM
  2. Crossing power sets
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 2nd 2009, 06:24 PM
  3. Power Sets
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: September 22nd 2008, 08:43 AM
  4. Induction with power sets
    Posted in the Number Theory Forum
    Replies: 6
    Last Post: April 28th 2008, 07:17 AM
  5. Power sets
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: July 22nd 2007, 07:21 PM

Search Tags


/mathhelpforum @mathhelpforum