a) int(A) intersect int(B) = int(A intersect B)
b) bd(A U B) is subset of bd(A) U bd(B)
c) Give examples of sets A and B where bd(A U B) = empty set and bd(A) = R = bd(B)
a) int(A) intersect int(B) = int(A intersect B)
b) bd(A U B) is subset of bd(A) U bd(B)
c) Give examples of sets A and B where bd(A U B) = empty set and bd(A) = R = bd(B)
a) Let . Then and . So such that and . Taking guarantees that . So and . See if you can prove the other direction.
b) Let . Then , . Note that .
Spoiler:
So . In particular, and , so .
c) Let and .
and consist of all with ; in other words, the real line. However, , and .