Prove that An(BnA)={}

To prove that An(BnA) = {}, we need to show that there are no elements in the intersection of B and A, and then calculate the intersection of A and the result of that.

First, let's show that there are no elements in the intersection of B and A. This means that there are no elements that are in both sets B and A. Therefore, AnB = {}.

Now, when we take the intersection of {} and A, we get {} because there are no elements in the intersection.

Therefore, An(BnA) = {}.

Overall, this proves that the intersection of A and the intersection of B and A is an empty set.