GATE CSE
First time here? Checkout the FAQ!
x
+6 votes
294 views

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)   | 294 views

2 Answers

+9 votes
Best answer
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)  
selected by
not reflexive in all cases
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:

Related questions



Top Users Mar 2017
  1. rude

    4758 Points

  2. sh!va

    3014 Points

  3. Rahul Jain25

    2830 Points

  4. Kapil

    2636 Points

  5. Debashish Deka

    2450 Points

  6. 2018

    1514 Points

  7. Vignesh Sekar

    1422 Points

  8. Akriti sood

    1314 Points

  9. Bikram

    1286 Points

  10. Sanjay Sharma

    1076 Points

Monthly Topper: Rs. 500 gift card

21,484 questions
26,812 answers
61,056 comments
23,065 users