Hello,

We have a not empty set X and call P(X) the power set of X. For the subsets A,B in X we define the symetric difference:

$\displaystyle A \Delta B = \left(A \setminus B \right) \cup \left(B \setminus A \right) $

To proof:

1.)

Proof that the triple $\displaystyle \mathfrak{P}(X),\Delta,\cap$ is a Ring

2.)

Is P(x) with this ringstructure a field?

3.) Proof that P(X) is a Vector Space over the Galois-field.

I have no idea

The first questions:

What is Delta?

Why is in the triple the intersection and not the union like in the definition?

How should I start?

Thanks for help

all the best

Herbststurm