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 ?
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 ?
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".