Let $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$,$A = \{1, 2, 3, 4\}$,$B = \{2, 4, 6, 8\}$,and $C = \{3, 4, 5, 6\}$. Find $(A')'$.

For each positive real number $\lambda$,let $A_\lambda$ be the set of all natural numbers $n$ such that $|\sin(\sqrt{n+1}) - \sin(\sqrt{n})| < \lambda$. Let $A_\lambda^c$ be the complement of $A_\lambda$ in the set of all natural numbers. Then,

$A$ and $B$ are events such that $P(A)=0.42$,$P(B)=0.48$ and $P(A \cap B)=0.16$. Determine $P(\text{not } A)$.

Draw an appropriate Venn diagram for the following: $(A \cup B)'$

Fill in the blanks to make each of the following a true statement:
$A \cup A^{\prime} = \ldots$

Consider the experiment of rolling a die. Let $A$ be the event 'getting a prime number' and $B$ be the event 'getting an odd number'. Write the set representing the event 'not $A$'.