Exercise 4, § 1

a) Give an example on the real line of two open sets $A, B$ such that the four sets $A \cap \overline{B}, B \cap \overline{A}, A \cap B$ and $\overline{A} \cap \overline{B}$ are all distinct.

b) Give an example of two intervals $A, B$ on the real line, such that $A \cap \overline{B}$ is not contained in $A \cap B.$