what are the ways on how to describe a relation?

Let A and B denote two sets. A relation from A to B is a subset of A x B. If R is a relation from A to B, then R is, by definition of Cartesian product, a set of ordered pairs, (a, b), where 'a' is an element of A & 'b' is an element of B.

Note: If there are n sets, say, A1, A2, ...,An, then a relation will consist of ordered n-tuples, (a1, a2, ...an), where 'a1' is an element of A1, 'a2' is an element of A2, ...,& 'an' is an element of An.

Relations can have some (but not all) of the following properties:

Transitive (aRb and bRc implies aRc)

Reflexive (aRa)

Symmetric (aRb and bRa implies a=b)

Anti-symmetric (can't recall exact form...sorry)

Trichotomous (sp?) (one of the following holds: aRb, bRa or a=b)

If said relation is a function, then it can be injective, surjective, or a bijection (1-1, onto, or 1-1 correspondence, respectively).

1. by asking

2. by observing

3. by reading and viewing visual aids

4. by being in the relationship itself

Love?

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Tables, graphs, and functions.

Doug