Multiple choice

A relation R is defined on ordered pairs of integers as follows: (x,y) R (u,v) if x < u 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
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A Correct answer
Explanation

An essential condition for Partial order, Total order and Equivalence Relation is Reflexive property. The given set is not reflexive as $\forall x, y \in I, \therefore $(x,y) is not related to (x,y)

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