Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

No-data Group Title

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.

  • one year ago
  • one year ago

  • This Question is Closed
  1. joemath314159 Group Title
    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.

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

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

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

    I'm ashamed this is actually the binomial theorem

    • one year ago
  4. sirm3d Group Title
    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.

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

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

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

    thank you @sirm3d

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

    YW

    • one year ago
    • Attachments:

See more questions >>>

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.