A subset is a set with fewer or equal elements then another set; where every element in the small set is also a member of the other set.

Notation

To express that a given set is a subset of another set the symbol is used. For example given two sets and stating that the set is a subset of the set could be written as . can be quantified as .

To express that a given set is not a subset of another set the symbol is used. For example given the previous examples sets stating that is not a subset of could be written as . can be quantified as .

Proper Subset

If the subset of a set is not equal to then the subset is said to be a proper subset. To express this relationship the symbol is used. For example to express that is a proper subset of it could be written as . could be quantified as .