Question
Tue June 19, 2012 By: Minu Joseph

# for any relation of set a to set b,can we say that the domain of this relation is always set a?please explain with an example.

Wed June 20, 2012
Yes, for any relation of set a to set b, we can say that the domain of this relation is always set a.
A relation is a subset of ordered pairs drawn from the set of all possible ordered pairs (of elements of two other sets, which we normally refer to as the Cartesian product of those sets). Formally, R is a relation if R ? {(x, y) | x ? X, y ? Y}
for the domain X and codomain Y.

The relation is defined only for the characterstic which has a relation with the elements of set A. Another way of looking at it is:
if the domain is a set Fruits = {apples, oranges, bananas} and the codomain is a set Flavors = {sweetness, tartness, bitterness}, the flavors of these fruits form a relation: we might say that apples are related to (or associated with) both sweetness and tartness, while oranges are related to tartness only and bananas to sweetness only. (We might disagree somewhat, but that is irrelevant to the topic of this book.) Notice that "bitterness", although it is one of the possible Flavors (codomain), is not really used for any of these relationships; so it is not part of the range {sweetness, tartness}.
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