Universal and Empty Set

Q1: What is the complement of a set $A$?
A1: The complement of a set $A$ is the set that contains all elements that do not belong to A.

$A^c=\{ x: x\not\in A\}$

It follows that:
$(A^c)^c=A$

Q2: What is the universal set?
A2: The universal set $\Omega$ is the set that contains all conceivable elements.
Hence, $A \cup A^c = \Omega$

Q3: What is the complement of the universal set?
A3: The empty set {} is the complement of the universal set. The empty set contains no elements.
Hence, $A \cap A^c = \{\}$