I have to finish this proof.

Let and be sets.

Let be the symmetric difference of those sets.

THM: .

Prove the above theorem by filling in the missing _____.

Proof(Direct)

Assume 1.) _______

Show 2.) _______

Let . Show .

Case 1:

3.) ___________________________________

Case 2:

4.) ___________________________________

(<-- should be backwards, but not sure how to do it in latex).

Similarly

Q.E.D

So 1 and 2 are easy, it's 3 and 4 that are rough.

1.)

2.)