1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Combinatorics and sets 2

  1. Dec 2, 2016 #1
    1. The problem statement, all variables and given/known data

    Given {1,2,...,n}, n is an even number. What are all the possible subsets that contain only even numbers? (Notice that ∅ is also defined as such a subset).

    2. Relevant equations

    2n - all possibilities for group A with n objects

    3. The attempt at a solution

    I think the answer is 2n/2 .... to include just even numbers. Is my reasoning correct?
     
  2. jcsd
  3. Dec 2, 2016 #2

    FactChecker

    User Avatar
    Science Advisor
    Gold Member

    You should add a few sentences to explain your reasoning. And the question is "what are", not "how many", so can you say something more about them?.
     
  4. Dec 3, 2016 #3
    Just bad translation on my part. "How many" is more correct. As for reasoning, we were taught in class that for n objects, you have 2n possibilities for subsets. So I thought that because we have n/2 objects (we want only even numbers) 2n/2 is the answer.
     
  5. Dec 3, 2016 #4

    FactChecker

    User Avatar
    Science Advisor
    Gold Member

    That is better. It never hurts to add a brief explanation like that.
     
  6. Dec 3, 2016 #5
    But is it correct?
     
  7. Dec 3, 2016 #6

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    It is correct. The odd numbers are irrelevant.
     
  8. Dec 3, 2016 #7
    Hmm ok. But what about ∅ ? If it is even, it should be included, but it does not seem to be included in {1...n}...
     
  9. Dec 3, 2016 #8

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    That's the empty set. That is included as one of the ##2^n## subsets. If you are looking for non-empty subsets then there are only ##2^n -1## of those.

    In this case you were explicitly told to count the empty set.
     
  10. Dec 3, 2016 #9
    Oh now I got it. Thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Combinatorics and sets 2
  1. Spanning sets in R^2 (Replies: 10)

  2. Combinatorics and sets (Replies: 18)

Loading...