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A relation R is defined on ordered pairs of integers as follows: $$(x,y)R(u,v) \text{ if } x<u \text{ and } y>v$$ Then R is:

  1. Neither a Partial Order nor an Equivalence Relation
  2. A Partial Order but not a Total Order
  3. A total Order
  4. An Equivalence Relation
asked in Set Theory & Algebra by Loyal (4k points)   | 304 views

2 Answers

+9 votes
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ans is (A).. because the relation is not reflexive.. which is a necessary condition for both partial order and equivalence realtion..!!
answered by Loyal (4.7k points)  
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not reflexive in all cases
For reflexivity, (X,Y) R (X,Y) , which here requires x<x and y<y and this is not possible in this relation.
0 votes
For a relation to be partial order or equivalence relation it must be reflexive.
i.e. (x,y) is some element of the set then (x,y)R(x,y), but this doesn't satisfy the given condition of x<x, y>y

Option A
answered by Active (1.6k points)  
Answer:

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