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

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,

Taking the set of natural numbers as the universal set,write down the complement of the following set:
$A = \{ x: x \ge 7 \}$

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 $(A')'$.

Taking the set of natural numbers as the universal set,write down the complement of the following set: $\{x: x+5=8\}$

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