Suppose that A and B are subsets of ℝ such that A is open and B is closed. Prove that A-B is open and B-A is closed. hint: use the fact that if X and Y are subsets of ℝthen X-Y=X∩(ℝ-Y). PLEASE SHOW ME THE LIGHT!!
For set difference $\displaystyle A\backslash B = A \cap B^c \,\& \,B\backslash A = B \cap A^c$.
Recall that the complement of a closed set is an open set and the intersection of two open sets is an open set.
Recall that the complement of an open set is a closed set and the intersection of two closed sets is a closed set.
This is my own take on this.
These are questions about basic topology.
I do not think that topics in topology have any place in a course on discrete mathematics.
Your instructor gave you something beyond your grasp.
The sad truth is: it may enhance her/his on importance without doing anything for you.