NTA UGC NET DEC2022 Paper2
October 3, 2023DigitalLogicDesign
October 3, 2023NTA UGC NET DEC2022 Paper2
Question 2

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
(x,y)R(u,v) if x < u and y > v. Then R is
Neither a partial order nor an equivalence relation


A partial order but not a total order


A total order


An equivalence relation

Question 2 Explanation:
A binary relation is an equivalence relation on a nonempty set S if and only if the relation is reflexive(R), symmetric(S) and transitive(T).
A binary relation is a partial order if and only if the relation is reflexive(R), antisymmetric(A) and transitive(T).
From the given relation, it is neither partial order nor equivalence relation.
A binary relation is a partial order if and only if the relation is reflexive(R), antisymmetric(A) and transitive(T).
From the given relation, it is neither partial order nor equivalence relation.
Correct Answer: A
Question 2 Explanation:
A binary relation is an equivalence relation on a nonempty set S if and only if the relation is reflexive(R), symmetric(S) and transitive(T).
A binary relation is a partial order if and only if the relation is reflexive(R), antisymmetric(A) and transitive(T).
From the given relation, it is neither partial order nor equivalence relation.
A binary relation is a partial order if and only if the relation is reflexive(R), antisymmetric(A) and transitive(T).
From the given relation, it is neither partial order nor equivalence relation.
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