Mathematical Relations?

Today we begin Module 7 by looking at 'relations'. I thought I'd start by taking an example from Wikipedia to get you thinking about how things can be 'related'.

Consider the relationship, involving three roles that people might play, expressed in a statement of the form "X thinks that Y likes Z ". The facts of a concrete situation could be organized in a Table like the following:

An informal example of relations

Person X Thinks Person Y Likes Person Z

Alice	Bob	Denise
Charles	Alice	Bob
Charles	Charles	Alice
Denise	Denise	Denise

Each row of the Table records a fact or makes an assertion of the form "X thinks that Y likes Z ". For instance, the first row says, in effect, "Alice thinks that Bob likes Denise". The Table represents a relation S over the set P of people under discussion:
P = {Alice, Bob, Charles, Denise}.
The data of the Table are equivalent to the following set of ordered triples:
S = {(Alice, Bob, Denise), (Charles, Alice, Bob), (Charles, Charles, Alice), (Denise, Denise, Denise)}.

Now for some notes...