A community for students.
Here's the question you clicked on:
 0 viewing
rishabh.mission
 3 years ago
Let A = Q x Q , Q being the set of rationals . Let ‘*’ be a binary operation
on A , defined by (a, b) * (c , d) = ( ac , ad + b) . Show that
(i) ‘*’ is not commutative (ii) ‘*’ is associative
(iii The Identity element w.r.t ‘*’ is ( 1 , 0)
rishabh.mission
 3 years ago
Let A = Q x Q , Q being the set of rationals . Let ‘*’ be a binary operation on A , defined by (a, b) * (c , d) = ( ac , ad + b) . Show that (i) ‘*’ is not commutative (ii) ‘*’ is associative (iii The Identity element w.r.t ‘*’ is ( 1 , 0)

This Question is Closed

sirm3d
 3 years ago
Best ResponseYou've already chosen the best response.1(i) (a,b) * (c,d) = (ac, ad + b) (c,d) * (a,b) = (ca,cb + d) (ac, ad + b) \(\neq\) (ca, cb + d) therefore it is not commutative

rishabh.mission
 3 years ago
Best ResponseYou've already chosen the best response.0thanks bro and how i solve (ii) part?

sirm3d
 3 years ago
Best ResponseYou've already chosen the best response.1compute (a,b) * ((c,d) * (e,f)) compute ((a,b) * (c,d)) * (e,f) compare the two ordered pairs if they are equal

sirm3d
 3 years ago
Best ResponseYou've already chosen the best response.1(a,b) * ((c,d) * (e,f)) = (a,b) * (ce, cf + d) = (ace, a(cf + d) + b) ((a,b) * (c,d)) * (e,f) = (ac, ad + b) * (e,f) = (ace, acf + (ad + b)) the two ordered pairs are the same, therefore * is associative

rishabh.mission
 3 years ago
Best ResponseYou've already chosen the best response.0thnanks again @sirm
Ask your own question
Sign UpFind 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
 Engagement 19 Mad Hatter
 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.