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:
$\{ x:x$ is a positive multiple of $3\} $
Fill in the blanks to make each of the following a true statement :
$A \cup A^{\prime}=\ldots$
If $U =\{1,2,3,4,5,6,7,8,9\}, A =\{2,4,6,8\}$ and $B =\{2,3,5,7\} .$ Verify that
$(A \cap B)^{\prime}=A^{\prime} \cup B^{\prime}$
If $A$ and $B$ be any two sets, then $(A \cap B)'$ is equal to
Taking the set of natural numbers as the universal set, write down the complements of the following sets:
$\{x: 2 x+5=9\}$