Solution:An equivalence relation on set x is a subset of x*x, i.e., a collection R of ordered pairs of elements of x, satisfying certain properties. Write "xRy" to mean (x, y) is an element of R and We say "x is related to y. Then the properties are Reflexive, Symmetric, Transitive.
An partial order relation on a set x is a subset of x*x, satisfying certain properties. The properties are Reflexive, Anti-Symmetric, Transitive.
An total order relation a set x is a subset of x*x, satisfying certain properties. The properties are Reflexive, Anti-Symmetric, Transitive, Comparability. As given in question, a relation "R" is defined on ordered pairs of integers as : (x, y) R (u, v) if x < u and y > v, Reflexive property is not satisfied here, because there is > or = v (or x = v and y = v) kind of relation among elements of sets then reflexive property could have been satisfied. Since reflexive property in not satisfied here, so given relation cannot be equivalence, partial order or total order relation. So, option (a) is correct.