Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

sasogeek

  • 2 years ago

what's the easiest way to determine whether the binary operation * is associative, if * is defined by \(x*y=\frac{x+y}{1+xy} \)

  • This Question is Closed
  1. NotSObright
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Define associativity

  2. sasogeek
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    x*(y*z)=(x*y)*z ... if it's associative, then the right hand side should be equal to the left hand side

  3. NotSObright
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    It is associative i did it by verifying LHS=RHS Although intuition pointed it right away

  4. sasogeek
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    well is that the easiest way...? i was thinking maybe there's a faster method

  5. Mr.Math
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    It clearly follows from the associativity of addition and multiplication.

  6. sasogeek
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    what do u mean by that?

  7. Mr.Math
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I mean \((x*y)*z=\frac{(x+y)+z}{1+(xy)z}=\frac{x+(y+z)}{1+x(yz)}=x*(y*z).\)

  8. sasogeek
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ohhh okay, well i was doing some weird workings but the answer was quite obvious right from the beginning :) thanks

  9. Mr.Math
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    You're welcome.

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

    Search OpenStudy
    • 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.