Monday, January 15, 2007
posted by man at 10:51 p.m.
To late for posting.lol!Well this is last mondays lesson.Relation(Domain and Range)

"Relation"

A relation is any subset of a Cartesian product. For instance, a subset of , called a "binary relation from to ," is a collection of ordered pairs with first components from and second components from , and, in particular, a subset of is called a "relation on ." For a binary relation , one often writes to mean that is in .

Eg.

(2,0),(1,5),(3,8),(4,1) ...(any set of ordered pairs are "relation")

The concept of a relation is a generalization of 2-place relations, such as the relation of equality, denoted by the sign "=" in a statement like "5 + 7 = 12," or the relation of order, denoted by the sign "<" in a statement like "5 < 12". the concept of a relation is a generalization of 2-place relations, such as the relation of equality, denoted by the sign "=" in a statement like "5 + 7 = 12," or the relation of order, denoted by the sign "<" in a statement like "5 < 12".

Relations are classified according to the number of sets in the cartesian product, in other words the number of terms in the expression:

Unary relation or property: L(u)

Binary relation: L(u, v) or u L v

Ternary relation: L(u, v, w)

Quaternary relation: L(u, v, w, x)

Domain and Range

Domain:

For a function f defined by an expression with variable x, the implied domain of f is the set of all real numbers variable x can take such that the expression defining the function is real. The domain can also be given explicitly.

Range:

The range of f is the set of all values that the function takes when x takes values in the domain.
The y-values.

This list of points, being a relationship between certain x's and certain y's, is a relation. The domain is all the x-values, and the range is all the y-values. You list the values without duplication:
{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)} This are the set of numbers.

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

You can see how we put the numbers in domain and range. All the x were put to domain and all y were put in range..