Q: What is the relation of a set of y-coordinates?

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An equivalence relation on a set is one that is transitive, reflexive and symmetric. Given a set A with n elements, the largest equivalence relation is AXA since it has n2 elements. Given any element a of the set, the smallest equivalence relation is (a,a) which has n elements.

A relation is defined as a set of ordered pairs. A function is a special kind of relation ...

Yes. The set of functions is a subset of the set of relations.

The relation, between two sets of objects, is a mapping which associates elements of the first set to those of the second set.

No, it is not.

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It is the set on which the relation is defined to the set which is known as the range.

If a set of ordered pairs is not a relation, the set can still be a function.

A relation doesn't have an "output value", in the sense that a function does. A set of values is either part of the relation, or it isn't.

A set of ordered pairs is a relation. Or Just simply "Coordinates"

It is the domain of the relation.

A relation is a set of ordered pairs

The set of output values of a function or relation is the range

An equivalence relation on a set is one that is transitive, reflexive and symmetric. Given a set A with n elements, the largest equivalence relation is AXA since it has n2 elements. Given any element a of the set, the smallest equivalence relation is (a,a) which has n elements.

A relation R is a set A is called empty relation if no element of A is related to any element of R

The Range is the set of all possible output values of a function or relation.

A relation is defined as a set of ordered pairs. A function is a special kind of relation ...

Yes. The set of functions is a subset of the set of relations.