A group that's a collection of sets

[halvizo1031]

Homework Statement

Let S be a set of things and let P be the set of subsets of S. For A,B in P, define
A*B=[(S-A)intersection B] union [A intersection (S-B)]
I'm suppose to show that (p,*) is commutative, find the identity, and given that A is a subset of S, find the inverse of A. How do i even start this?

Homework Equations

The Attempt at a Solution

I need help starting it.

 

[Donaldos]

Show that $$A*B=B*A$$.

Find $$I \in S$$ such that $$A*I=I*A=A , \quad\forall A \in P$$.

Find $$B \in S$$ such that $$A*B=I$$.

 

[lanedance]

did you try what i suggested in your last post? (the exact same question)

https://www.physicsforums.com/showthread.php?t=347210

it was also suggested to use the fact unions & intersections are commutative operations

 

[halvizo1031]

Show that $$A*B=B*A$$.

Find $$I \in S$$ such that $$A*I=I*A=A , \quad\forall A \in P$$.

Find $$B \in S$$ such that $$A*B=I$$.

I'm sorry but i couldn't understand what you wrote. And by that i mean that i can't read it. Could you rewrite it please?

 

[lanedance]

then try the follwing multiplications: A with the empty set & A with its complement