Results 1 to 3 of 3

Math Help - Subsets and Combinatorics

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    14

    Subsets and Combinatorics

    What is the number of subsets (including the empty set) of {1,2,3,...,12} that are contained in (at least) one of the following sets:

    {1,2,3,4,5,6}, {5,6,7,8}, {7,8,9,10,11,12}, and {1,6,11,12}

    Any ideas would be greatly appreciated. Thanks for your time.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,517
    Thanks
    771
    You could try using the Inclusion–exclusion principle and note that \mathcal{P}(A)\cap\mathcal{P}(B)=\mathcal{P}(A\cap B).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2010
    Posts
    14
    Using the Inclusion-Exclusion Principle:

    2^6 + 2^4 + 2^6 + 2^4 - 2^2 -2^2 - 2^2 - 2^2 - 2^1 - 2^0 + 2^0 + 2^0 + 2^1 - 2^0 = 144

    However, I also wrote out all the possible subsets, counted and removed the duplicates and found the answer to be 145.

    Is the above calculation incorrect, or am I just a horrible counter... haha
    Thanks!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Combinatorics and subsets #2
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: March 31st 2011, 11:58 AM
  2. Combinatorics and subsets #1
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: March 31st 2011, 11:58 AM
  3. How many subsets
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: May 17th 2010, 05:41 AM
  4. subsets
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: December 7th 2009, 01:24 PM
  5. Subsets
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: October 1st 2009, 07:54 PM

Search Tags


/mathhelpforum @mathhelpforum