Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
Prove that if an ordered pair of ordered pairs ((a,b),(c,d)) has the property ad=bc, then this property is transitive, i.e. if another ordered pair((c,d),(f,g)) is in this relation, then ((a,b),(f,g)) is in this relation as well, such that ag = bf.
 one year ago
 one year ago
Prove that if an ordered pair of ordered pairs ((a,b),(c,d)) has the property ad=bc, then this property is transitive, i.e. if another ordered pair((c,d),(f,g)) is in this relation, then ((a,b),(f,g)) is in this relation as well, such that ag = bf.
 one year ago
 one year ago

This Question is Closed

windsylphBest ResponseYou've already chosen the best response.0
The actual proof, I know I have to show that ag = bf. But how do you actually show that knowing ad = bc and cg = df? Haha I know too that this might be trivial, but for some reason I just can't wrap my mind around it.
 one year ago

micrad25Best ResponseYou've already chosen the best response.0
Proofs can be difficult because there are so many to choose from but what i did was i made flashcards on all the proofs (in the back of the book) and memorized them. There is a lot but if you memorize one a day you will be a pro by the end of the year!
 one year ago

micrad25Best ResponseYou've already chosen the best response.0
But if your teacher doesn't require that you know them, its your choice.
 one year ago

ZarkonBest ResponseYou've already chosen the best response.1
what does ((c,d),(f,g)) tell you?
 one year ago

anonymoustwo44Best ResponseYou've already chosen the best response.0
let (a,b), (c,d), and (f,g) be any ordered pairs, such that ((a,b),(c,d)) and ((c,d),(f,g)) so that ab=cd and cd=fg. Now we know from basic algebra, ab=fg, hence ((a,b),(f,g)) when ((a,b),(c,d)) and ((c,d),(f,g)), therefore the property is transitive
 one year ago

ZarkonBest ResponseYou've already chosen the best response.1
@anonymoustwo44 ((a,b),(c,d)) has the property ad=bc ... not ab=cd
 one year ago

windsylphBest ResponseYou've already chosen the best response.0
as I've said above, from ((c,d),(f,g)), we know that cg = df. Then..?
 one year ago

ZarkonBest ResponseYou've already chosen the best response.1
ad = bc multiply by g adg=bcg using cg=df we get bcg=bdf thus adg=bdf divide by d ag=bf you should look at the case where d=0 to validate that everything still works out.
 one year ago

windsylphBest ResponseYou've already chosen the best response.0
Thank you. It is indeed trivial then. I'm sorry for the trouble, for some reason I just couldn't think of that earlier..
 one year ago

windsylphBest ResponseYou've already chosen the best response.0
Also, I forgot to remark that the components of the ordered pairs should only be positive integers, so I don't have to show the case where d = 0.
 one year ago
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
 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.