October 3, 2023
October 3, 2023
October 3, 2023
###### Digital-Logic-Design
October 3, 2023
 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
 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
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.
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.