Math Is Fun Forum

Al-Allo

Member

Registered: 2012-08-23

Posts: 324

Some logic question

Hi, there's something that have been bugging me.

If we have quantities A, C, E

And if we have quantities B, D, F

And if we take the equimultiples G, H, K from A, C, E

And if we take the equimultiples L, M, N from B, D, F

And we show that whenever G is superior to L, then H is going to be superior to M. And if equal, equal. And if less, then less.

And we show that whenever K is superior to N, then H is going to be superior to M. And if equal, equal. And if less, then less.

Then, how can you be sure that whenever G is superior L, K is going be superior to N. If equal, equal. And if less, then less.

Usually we have a situation of if X is equal to B and if Y is equal to B, then X is going to be equal to Y. (This is not hard to digest, obviously)

But in the situation just described, i'm having a hard time digesting this... I have no problem understanding the statement but the conclusion is hard to digest or to be accepted by my mind.

Thank you!

Last edited by Al-Allo (2015-07-27 07:22:35)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Some logic question

hi Al-Allo

I'm not understanding you.

Let's say A = 8, C = 2 and E = 4.  Suppose the multiplier is 7.

Then G = 56, H = 14 and K = 28.

Now suppose  B = 1, D = 3 and F = 2 with multiplier 5.

Then L = 5, M = 15 and N = 10.

G > L (56 > 5) but H is not greater than M ( 14 < 15).

So I guess that was not what you meant.  Please clarify.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Al-Allo

Member

Registered: 2012-08-23

Posts: 324

Re: Some logic question

hi Al-Allo

I'm not understanding you.

Let's say A = 8, C = 2 and E = 4.  Suppose the multiplier is 7.

Then G = 56, H = 14 and K = 28.

Now suppose  B = 1, D = 3 and F = 2 with multiplier 5.

Then L = 5, M = 15 and N = 10.

G > L (56 > 5) but H is not greater than M ( 14 < 15).

So I guess that was not what you meant.  Please clarify.

Bob

Yes, i'm not saying that taking every number is going to work. The basic idea is that if you have a proportion of the type :

3/2 = 6/4 = 12/8

with 7 :

21 , 42 , 84

with 5 :

10 , 20, 40

21 > 10 , 42 > 20 and 84 > 40.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Some logic question

So, in general, you have

And you multiply the numerators by, say, p and the denominators by q giving:

G = pa ,     H = pc ,       K = pe

and

L = qb ,     M = qd ,       N = qf

so

So if G > L then H > M and K > N etc.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob