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Equivalence Classes

You've actually dealt with modular arithmetic for most of your life: the clock face represents arithmetic with modulus 12. If you've ever served in the...

Equivalence Relations

We ordinarily are completely comfortable writing things like     The symbols and , though, are definitely not the same. One of them, for example,...

Graphing Relations

There are two ways to think about drawing a picture of a relation on a set . if We can draw relations on , because...

Properties of Relations

Now we are ready to consider some properties of relations. Our interest is to find properties of, e.g. motherhood. To do this, remember that we...

Operations on Relations

Besides the ordinary set operations, there are special operations we can perform on relations. Definition. The inverse of a relation from to is the relation...

Basics of Relations

What's a relation? Definition.  A relation from the set to the set is a(ny) subset of . We call the source and the target or...