Answer
Done below.
Work Step by Step
a) $A \cup \emptyset = \{x : x \in A \vee x \in \emptyset \} = \{x : x \in A \vee F \} = \{x : x \in A\} = A$
b) $A \cap U = \{x : x \in A \wedge x \in U \} = \{x : x \in A \wedge T \} = \{x : x \in A\} = A$