Labelling sets in a Venn diagram

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The discussion revolves around labeling sets in a Venn diagram, specifically identifying sets A and B based on limited information. Set A is confirmed to be a collection of odd numbers, but the nature of set B remains unclear. Participants express skepticism about finding a pattern between the sets, suggesting that the task is more about labeling than identifying relationships. They propose labeling the intersection, union, and complements of the sets, despite the ambiguity in the provided data. The overall consensus is that there is insufficient information to derive a clear relationship for set B.
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Homework Statement


Label each set in the following Venn diagram as described in the attached pdf file.

Homework Equations


The Attempt at a Solution


Unable to find a relationship that can describe the second set B. Obviously set A is a collection of Odd numbers.
 

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Is this all the information there is? If so, I think the question is asking you to identify the unions, intersections, whatever. I doubt the fact that the numbers in A all happen to be odd is of any relevance.
 
Thanks for your reply. The question is asking to classify each set. There seems to be a pattern or relationship between the two sets that I can not figure out!
 
I find it extremely unlikely that you would be asked to find a pattern here. There just isn't enough data to go on, and it's not the sort of question likely to be asked in elementary set theory.
In your first post you said 'label the sets'. That's not the same as finding a pattern in them, and is a much more reasonable task. Trouble is, 'the sets' is rather vague. In the PDF, two sets are already labelled, A and B. What's unclear is which other sets are to be labelled, but you could obviously label the intersection of A and B, and universal set. You could also identify the union and the complements, though those might be harder to indicate in a drawing.
Are you quite sure there's no other information which might indicate which sets you are expected to label?
 
samirgaliz said:

Homework Statement


Label each set in the following Venn diagram as described in the attached pdf file.



Homework Equations





The Attempt at a Solution


Unable to find a relationship that can describe the second set B. Obviously set A is a collection of Odd numbers.

I think, clearly, they are looking for groupings such as:

set {567, 845, 931} is A AND NOT B
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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