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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.
Is the answer the power set of AxA?
2^36.
fresh_42 said:Yes.
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.Bipolar Demon said:
I do not understand this too. I am getting an empty set for it.
This follow-up question appears to be homework, so I do not want to blurt out what seems to be the expected answer.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.
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.
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.
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.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/
Bipolar Demon said:no not homework just personal reading. :)
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.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.
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.
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.
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).
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.
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.