UGCNET CSE December 2022: 2

Question

 

A relation '$R$ ' is defined on ordered pairs of integers as: $(x, y) R(u, v)$ if $x<u$ and $y>v$. Then $R$ is

• A. Neither a partial order nor an equivalence relation
• B. A partial order but not a total order
• C. A total order
• D. An equivalence relation

(Option $1 [39305]) 1$
(Option $2 [39306]) 2$
(Option $3 [39307]) 3$
(Option $4 [39308]) 4$

Answer Given by Candidate : $4$

Answer 1

This question is easy  by checking just one property . but first see what we need . 

for equivalence relation(RST PROPERTIES) , we need to check 3 properties 

1. REFLEXIVE 
2.  SYMMETRIC
3.  TRANSITIVE  as we can see it is not reflexive bcz, (x,y) is not related to (x,y) . so by just checking this we can say it is not equivalence. it is also not symmetric . bcz number can either be greater or lesser one at a time .. 

for partial order relation (RAT PROPERTIES) , we need to check 3 properties 

1. REFLEXIVE
2. ANTISYMMETRIC
3. TRANSITIVE

as we have already seen relation is not reflexive hence it not partial order relation .

we know , every total order is partial order but relation is not partial then also not total ..

Comments

So, clearly, it is $A$