# Relation

• Nov 4th 2012, 05:48 PM
lol888
Relation
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 ?
• Nov 4th 2012, 06:25 PM
topsquark
Re: Relation
What have you been able to do so far?

-Dan
• Nov 4th 2012, 06:33 PM
Plato
Re: Relation
Quote:

Originally Posted by lol888
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?
• Nov 4th 2012, 06:55 PM
Deveno
Re: Relation
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".
• Nov 4th 2012, 07:03 PM
Plato
Re: Relation
Quote:

Originally Posted by Deveno
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.