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

Let $U$ be the universal set of all the students of Class $XI$ of a coeducational school and $A$ be the set of all girls in Class $XI$. Find $A'$.

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

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,

Let $A$ and $B$ be two non-empty subsets of a set $X$ such that $A$ is not a subset of $B$,then

If $A$ is any set,then: