Let A = {1,2,3,4,5,6.} # of many different relations possible

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Discussion Overview

The discussion revolves around the question of how many different relations are possible for the set A = {1, 2, 3, 4, 5, 6}. Participants explore the concept of relations in set theory, particularly focusing on the power set of AxA and the implications of including or excluding certain elements in the relations.

Discussion Character

  • Exploratory
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant suggests that the number of different relations is represented by the power set of AxA, calculating it as 2^36.
  • Several participants agree with the calculation of 2^36 as the number of relations.
  • Another participant expresses confusion, initially thinking the answer is an empty set, but later clarifies that it cannot be empty since every element relates to every other element except itself.
  • A participant introduces a hypothetical relation, comparing it to the idea that "every hand can wash every hand, but not itself," and questions its mathematical representation.
  • Some participants indicate that the question may be perceived as homework-related, leading to caution in providing direct answers.
  • One participant clarifies that their inquiry is for personal reading and not for an actual homework assignment, referencing a book that includes the question.
  • There is a discussion about the ambiguity of what constitutes homework on the forum, with references to forum guidelines regarding homework-like questions.

Areas of Agreement / Disagreement

Participants generally agree on the calculation of the number of relations as 2^36, but there is disagreement regarding the interpretation of certain aspects of relations, particularly concerning the inclusion of self-relations and the nature of the question as homework-related.

Contextual Notes

Some participants express uncertainty about the definitions and implications of relations, particularly in the context of excluding self-relations. There is also a noted ambiguity regarding the classification of the question as homework or personal inquiry.

Who May Find This Useful

This discussion may be useful for individuals studying set theory, particularly those interested in the concept of relations and the nuances of homework-related inquiries in academic forums.

Logical Dog
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How many different relations are possible? Is the question.

Is the answer the power set of AxA?
2^36.
 
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Yes.
 
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fresh_42 said:
Yes.

HLnt9Fu.png


I do not understand this too. I am getting an empty set for it.
 
Bipolar Demon said:
HLnt9Fu.png


I do not understand this too. I am getting an empty set for it.
No, not an empty set, because everything is related to everything without itself. The main diagonal is missing. But I cannot think of a familiar relation.
Something like: every hand can wash every hand, but not itself. However, what is this mathematically?

Edit: e.g. the domain of ##(x,y) \longmapsto (x-y)^{-1}##.
 
Last edited:
fresh_42 said:
No, not an empty set, because everything is related to everything without itself. The main diagonal is missing. But I cannot think of a familiar relation.
This follow-up question appears to be homework, so I do not want to blurt out what seems to be the expected answer.
 
jbriggs444 said:
This follow-up question appears to be homework, so I do not want to blurt out what seems to be the expected answer.
Got it.
 
jbriggs444 said:
This follow-up question appears to be homework, so I do not want to blurt out what seems to be the expected answer.

no not homework just personal reading. :) I was going over relations once more as I never got it completely the first time. It is a question in this book (and I just noticed that it has solutions there too but they are only for ODD numbered questions
http://www.people.vcu.edu/~rhammack/BookOfProof/
 
Bipolar Demon said:
no not homework just personal reading. :) I was going over relations once more as I never got it completely the first time. It is a question in this book (and I just noticed that it has solutions there too but they are only for ODD numbered questions
http://www.people.vcu.edu/~rhammack/BookOfProof/
The difficulty is that the the "homework" umbrella on these forums encompasses both material that is actual homework and material that is homework-like, even though it may not be an assigned homework problem in a course that is currently being taken.

See the sticky posting at the top of this forum: https://www.physicsforums.com/threa...mework-or-any-textbook-style-questions.42532/
 
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Bipolar Demon said:
no not homework just personal reading. :)

jbriggs444 said:
The difficulty is that the the "homework" umbrella on these forums encompasses both material that is actual homework and material that is homework-like, even though it may not be an assigned homework problem in a course that is currently being taken.
As jbriggs444 said, your post falls under the heading of "homework," which includes problems from books even if you are not in a course that uses that textbook.
 
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