No mathematician today would flatly refuse to accept the results of an enormous computation as an adequate demonstrat...

Dalaal March 2, 2020

same or different variables?

I am a bit confused about the method of determining which conditions should be given the same variable and those that shouldn't. FOr example, I gave the same variable to both the statements "would flatly refuse to accept the results of an enormous computation as an adequate demonstration of the truth of a theorem" and "refused to accept the results of a complex computer demonstration of a very simple mapping theorem." DO these statements allude to the same thing, why were they given different variables? Moreover, I gave different variables to the statements "strong belief that a simple theorem ought to have a shot, simple proof" and "required enormous proofs." That is because I considered the phrase "have a strong belief" to have added to the former statement something that the latter statement lacked. Why were they given the same variable?

Create a free account to read and take part in forum discussions.

Already have an account? log in

BenMingov March 18, 2020

Hi Dalaal, thanks for bringing this up.

This is quite a complex problem due to the elaborate wording used for each of the terms. I think there is no one size fits all rule when it comes to equating terms and writing them using the same variables, when they are worded differently in the passage. I think the best way to go about this is to use your judgment from passage to passage and see whether or not they mean the same thing and then equate them if they do.

In this case, I would say that both of your thoughts are valid and that it could be approached this way.

In looking at the answer choice and incorporating "strong belief" you would still land on the same deduction. I think sometimes, we omit some words from our symbols to avoid clutter, while noting mentally that strong belief is associated with "simple theorem, short proof"

You seem to have a good grasp of how to operate these question using conditional reasoning and quantifiers, so it may just be differences in preference of how one person approaches the diagram versus another. I think your thinking is correct here.

I hope this helps. Please let me know if you have any other questions.