Groups Further

Groups of Sets

Age 16 to 18 Challenge Level:

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.

Rose

Age 16 to 18 Challenge Level:

What groups of transformations map a regular pentagon to itself?

Poison, Antidote, Water

Age 14 to 18 Challenge Level:

Play the game of Poison, Antidote, Water to start to understand the mathematics of associativity and groups.