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If A then B then C
A
therefore C

2006-11-10 21:54:48 · 7 answers · asked by barkusmuhl 2 in Science & Mathematics Mathematics

7 answers

Yes.

The argument is valid but not perfectly worded.

Here A, B, C can be variables as others have pointed out or they are statements that are fulfilled in direct progression. In fact this is a form of the "Direct Proof"

Direct Proof example:

As an example we can claim that if we have A:={the addition of two odd numbers x, y | x+y} it will become an even number which can be statement C.

So by our knowledge that odd numbers can be written as
x = 2m+1 and y = 2n+1 where m, n are any integers we can use that as statement B. Hence B:={x = 2m+1 and y = 2n+1 where m, n are any integers}

Doing a little algebra we have
x+y = (2m+1) + (2n+1) = 2m + 2n + 2 = 2(m+n+1)

Now we can find out that (m+n+1) is an integer as by definition and we can call it "p" s.t. p=(m+n+1),
Hence x+y = 2(m+n+1) = 2p, and by our knowledge of numbers 2p is an even number. Hence C is fullfilled.

Thus like questioner's argument:
If A then B then C
A
therefore C.

And with my example and statements in quotations can be be replaced by letters A, B, and C:
If "you add two odd numbers" then "they are integers that can be written as the addition of two times another integer plus one which algebraically can be written as two times integer" then "you obtain a number which is even".
"You add two odd numbers"
therefore "you obtain a number which is even".
Q.E.D.

2006-11-10 23:16:49 · answer #1 · answered by ioniceclipse 2 · 2 0

No, because a valid argument has to make sense. That does not make sense. If A then B then C what? What's with the extra A? If you could reword it, then maybe I could help.

2006-11-11 06:08:05 · answer #2 · answered by Anonymous · 0 1

No because "then" is not a quantifying word. Then what? If you were to say something like:
If A equals B and B equals C then A equals C
that would be valid.
Or something like:
If A is less than B and B is less than C then A is less than C
that would be valid. You need a quantifying word instead of "then".

2006-11-11 06:00:24 · answer #3 · answered by zaffaris 5 · 0 2

I think it would somewhat be correct

a } b} c

a } c
is a near equivalent relation it however depends on how } are defined to represent/imply

2006-11-11 06:10:42 · answer #4 · answered by Sabure Kennedy 2 · 0 0

i am not sure..but i think it is correct...
if A then it should be B..and if B then it should be C..
so if A then it should it means it will reach to C

2006-11-11 06:04:14 · answer #5 · answered by thadu 5 · 0 0

Perhaps.

2006-11-11 06:01:57 · answer #6 · answered by ? 7 · 0 0

as far as i thnk YES

2006-11-11 06:03:56 · answer #7 · answered by Nas 2 · 0 0

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