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.