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## #1 2010-10-10 07:07:27

Jono
Guest

### Need Urgent help with relations

Let 'A' be the set of dogs at Edinburgh Dog Pound.

1) Describe A x A
2) Give an example of a relation on A.

## #2 2010-10-10 07:14:32

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Need Urgent help with relations

A x A is a set made from pairings of dogs. Any pairing of dogs must be included in the set, and order is important.

For example, if the Dog Pound held the dogs Fido, Rex and Spot, then A x A would be:

{ (Fido, Fido), (Fido, Rex), (Fido, Spot), (Rex, Fido), (Rex, Rex), (Rex, Spot), (Spot, Fido), (Spot, Rex), (Spot, Spot) }

One relation on A could be that for any x, y in A, x~y if their names are the same length.

You can define any relation on A in terms of a subset of A x A.
In this case, it would be:

{ (Fido, Fido), (Fido, Spot), (Rex, Rex), (Spot, Fido), (Spot, Spot) }

Why did the vector cross the road?
It wanted to be normal.

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