Let $\mathrm{U}$ be universal set of all the students of Class $\mathrm{XI}$ of a coeducational school and $\mathrm{A}$ be the set of all girls in Class $\mathrm{XI}$. Find $\mathrm{A}'.$
Since $A$ is the set of all girls, $A'$ is clearly the set of all boys in the class.
Now, we want to find the results for $(A \cup B)^{\prime}$ and $A^{\prime} \cap B^{\prime}$ in the followng example.
Taking the set of natural numbers as the universal set, write down the complements of the following sets:
$\{ x:x \in N$ and $2x + 1\, > \,10\} $
Draw appropriate Venn diagram for each of the following:
$(A \cap B)^{\prime}$
Taking the set of natural numbers as the universal set, write down the complements of the following sets:
$\{ x:x$ is a perfect square $\} $
Taking the set of natural numbers as the universal set, write down the complements of the following sets:
$\{ x:x$ is an odd natural number $\} $
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
$A^{\prime}$