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

• I
• Logical Dog
In summary, the conversation is about the concept of relations and possible ways to define them mathematically. The main question is how many different relations are possible, and the answer is 2^36. The conversation then delves into discussing a specific relation and whether it fits the criteria for a familiar relation or if it is a homework problem.
Logical Dog
How many different relations are possible? Is the question.

Is the answer the power set of AxA?
2^36.

Yes.

Logical Dog
fresh_42 said:
Yes.

I do not understand this too. I am getting an empty set for it.

Bipolar Demon said:

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/

Logical Dog
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.

Logical Dog

## 1. How many different relations are possible with the set A?

There are 26 = 64 different relations possible with the set A. This is because each element in the set can either be included or not included in a relation, leading to 2 choices for each element and thus 26 = 64 possible combinations.

## 2. What is the definition of a relation?

A relation is a set of ordered pairs where the first element of each pair is from one set, called the domain, and the second element is from another set, called the range.

## 3. Are all relations possible with the set A reflexive?

No, not all relations possible with the set A are reflexive. A relation is reflexive if every element in the domain is related to itself, but with the set A, there are 6 elements and only 4 of them can be related to themselves (1, 2, 3, and 4).

## 4. Can the set A have more than one reflexive relation?

Yes, the set A can have more than one reflexive relation. For example, the relation {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)} and the relation {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6), (1,2), (2,1), (3,4), (4,3), (5,6), (6,5)} are both reflexive relations for the set A.

## 5. How does the number of elements in the set affect the number of possible relations?

The number of elements in the set affects the number of possible relations exponentially. For a set with n elements, there are 2n possible relations. This means that as the number of elements increases, the number of possible relations increases at a rapidly growing rate.

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