anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Zarkon
  • Zarkon
where are you stuck?
anonymous
  • anonymous
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.
anonymous
  • anonymous
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!

Looking for something else?

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

More answers

anonymous
  • anonymous
But if your teacher doesn't require that you know them, its your choice.
Zarkon
  • Zarkon
what does ((c,d),(f,g)) tell you?
anonymous
  • anonymous
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
Zarkon
  • Zarkon
@anonymoustwo44 ((a,b),(c,d)) has the property ad=bc ... not ab=cd
anonymous
  • anonymous
as I've said above, from ((c,d),(f,g)), we know that cg = df. Then..?
Zarkon
  • Zarkon
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.
anonymous
  • anonymous
Thank you. It is indeed trivial then. I'm sorry for the trouble, for some reason I just couldn't think of that earlier..
anonymous
  • anonymous
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.

Looking for something else?

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