# open and closed sets proof

• Oct 28th 2008, 02:00 PM
gatesamatic
open and closed sets proof
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!!
• Oct 28th 2008, 02:19 PM
Plato
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.
• Oct 28th 2008, 04:07 PM
gatesamatic
Quote:

Originally Posted by Plato
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.

haha I don't know what this means. My discrete professor gave it to us an extra credit assignment. I can't figure out this neighborhood, boundary, etc etc stuff. Can anyone offer a completed proof?
• Oct 28th 2008, 05:19 PM
Plato
Quote:

Originally Posted by gatesamatic
My discrete professor gave it to us an extra credit assignment. I can't figure out this neighborhood, boundary, etc etc stu

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.