Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

No-data

  • one year ago

I was enumerating the elements of the power set of this set S:= {1,2,3,4,5} and I thought that the number of these elements could be obtained with this: \[\#\wp S = 1 + \sum_{k=1}^n {n\choose k} \] where \(n=\#S\) I saw that it holds for this set. But I'm not sure what if it could be applied to a different kind of set.

  • This Question is Closed
  1. joemath314159
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    That formula is right, but there is a much shorter formula for the number of elements in the power set of an n-element set. If write out the power sets for sets with 2, 3 and 4 elements, it should become clear what the shorter formula is.

  2. No-data
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yeah I know. The formula is \(2^n\)

  3. No-data
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I'm ashamed this is actually the binomial theorem

  4. sirm3d
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the binomial expansion of \((x+y)^n\) is \[\Large (x+y)^n=\sum_{k=0}^n \left(\begin{matrix}n \\ k\end{matrix}\right)x^ky^{n-k}\] put \(x=y=1\) and you'll get the answer to your question.

  5. No-data
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\#\wp S=2^{\#S}= \sum_{k=0}^{n} {n\choose k}\]

  6. No-data
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    thank you @sirm3d

  7. sirm3d
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    YW

  8. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.