Relation

Nov 2012
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0
UK
R on X={1,2,3,4,5}
R={(1,3 ), (1, 2), (1, 4), (2, 5), (2, 1), (4, 1), (3, 1), (3, 2), (5, 2), (5, 3)

determine relation is equivalence relation or not?

determine relation is a partial order or not ?
 
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topsquark

Forum Staff
Jan 2006
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What have you been able to do so far?

-Dan
 

Plato

MHF Helper
Aug 2006
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A={(1,3 ), (1, 2), (1, 4), (2, 5), (2, 1), (4, 1), (3, 1), (3, 2), (5, 2), (5, 3)}
determine relation is equivalence relation or notdetermine relation is a partial order or not ?
As written, this is a nonsense question.
There is no possible answer if the domain of the relation is not listed.
Can you tell us more about the question?
 

Deveno

MHF Hall of Honor
Mar 2011
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in order to DEFINE a relation R, you need to SPECIFY what SET R is a relation ON.

my guess is that the underlying set is S = {1,2,3,4,5}, but without knowing for sure, i am just speculating.

what i CAN tell you, is if an relation IS an equivalence on a set S, it contains all elements of SxS of the form (s,s), for each s in S (this set is called the DIAGONAL of S).

what i also can tell you is that partial orders are anti-symmetric: if aRb (that is, (a,b) is in R) and bRa (that is, (b,a) is in R) we have a = b.

these observations are pertinent to your question, but it's up to you to figure out "how".
 

Plato

MHF Helper
Aug 2006
22,507
8,664
in order to DEFINE a relation R, you need to SPECIFY what SET R is a relation ON.

my guess is that the underlying set is S = {1,2,3,4,5}, but without knowing for sure, i am just speculating.

what i CAN tell you, is if an relation IS an equivalence on a set S, it contains all elements of SxS of the form (s,s), for each s in S (this set is called the DIAGONAL of S).

what i also can tell you is that partial orders are anti-symmetric: if aRb (that is, (a,b) is in R) and bRa (that is, (b,a) is in R) we have a = b.

these observations are pertinent to your question, but it's up to you to figure out "how".
@Deveno, why should we have to guess?
Let's make the poster be clear as to exactly what the question is.
 
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