What is the Answer to 1/3(10) using Logic?

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Homework Help Overview

The discussion revolves around the interpretation of the expression \(\frac{1}{3}(10)\) using a specific logic framework, which is not clearly defined. The original poster references a previous statement \(\frac{1}{2}(5)=3\) and attempts to apply similar reasoning to derive a value for \(\frac{1}{3}(10)\).

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants question the validity of the logic used by the original poster, particularly the assertion that \(\frac{5}{2}=3\) can lead to further conclusions. There are requests for clarification on the rules or axioms that govern the logic being applied.

Discussion Status

There is ongoing exploration of the assumptions behind the original question. Participants are seeking to understand the underlying logic and whether additional context or rules are necessary to answer the question. Some express confusion about the implications of the statements made.

Contextual Notes

Participants note that the question lacks sufficient information to be answered definitively, as it appears to be derived from an informal source without clear axioms or rules. There is a recognition that the problem may rely on proportional reasoning, but this is not universally accepted among the participants.

adjacent
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Homework Statement


##\frac{1}{2}(5)=3## , based on this logic, what is ##\frac{1}{3}(10)##?

The Attempt at a Solution


In real life, ##\frac{1}{2}(5)=2.5## so
2.5 --> 3
Just like that, ##\frac{1}{3}(10)=\frac{10}{3}##
so
2.5 --> 3
10/3 -->x

Cross multiply---
x=4
I am not very sure whether this is correct or not. I don't know what logic this question assumes. Proportion or addition?
 
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You haven't described a logic yet. You have to state all the rules you are using. Just by stating that ##5/2=3## doesn't get you anywhere, because the only thing it implies is that ##5/2=3##, nothing else.
 
micromass said:
You haven't described a logic yet. You have to state all the rules you are using. Just by stating that ##5/2=3## doesn't get you anywhere, because the only thing it implies is that ##5/2=3##, nothing else.

I don't understand :confused:
 
adjacent said:
I don't understand :confused:

Can you list all the rules (axioms) of your system?
 
micromass said:
Can you list all the rules (axioms) of your system?
Are you asking what I assumed?
We know that(From the question) ##\frac{5}{2}=3=2.5## So what I assumed is
##3=k2.5## | ##k=1.2##
Let ##i## be the false(Logic of the question) value and ##r## be the true value
Then ##i=1.2r##
So ##x=1.2 \times \frac{10}{3}##
##x=4##
 
adjacent said:
I don't understand :confused:
5/2 = 3 is simply a statement - there is nothing you can extrapolate from this to answer your question. The real number system obeys a set of axioms, so similarly there must exist a set of axioms that your system has to adhere to. Was there more given in the question or in an earlier exercise perhaps?
 
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CAF123 said:
Was there more given in the question or in an earlier exercise perhaps?
That is the problem. I wrote exactly as the question was written. This is not an exercise, I saw this from the internet.

So the question cannot be answered without knowing what rules it obeys();?
 
adjacent said:
That is the problem. I wrote exactly as the question was written. This is not an exercise, I saw this from the internet.

So the question cannot be answered without knowing what rules it obeys();?

The question as you asked in your OP cannot be answered. You need more information (such as other rules that the system obeys).
 
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Oh, I get it now. I see questions like these all over the internet. They normally use proportion.
Anyway,thanks
 

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