This article only skims the surface of Galois theory and should
probably be accessible to a 17 or 18 year old school student with a
strong interest in mathematics.
Explore the properties of some groups such as: The set of all real
numbers excluding -1 together with the operation x*y = xy + x + y.
Find the identity and the inverse of the element x.
The binary operation * for combining sets is defined as the union
of two sets minus their intersection. Prove the set of all subsets
of a set S together with the binary operation * forms a group.