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

$(A \cup C)^{\prime}$

Let $U=\{1,2,3,4,5,6\}, A=\{2,3\}$ and $B=\{3,4,5\}$

Find $A^{\prime}, B^{\prime}, A^{\prime} \cap B^{\prime}, A \cup B$ and hence show that $(A \cup B)^{\prime}=A^{\prime} \cap B^{\prime}$

Draw appropriate Venn diagram for each of the following:

$A^{\prime} \cup B^{\prime}$

If $A$ and $B$ be any two sets, then $(A \cap B)'$ is equal to

Fill in the blanks to make each of the following a true statement :

$A \cap A^{\prime}=\ldots$

Taking the set of natural numbers as the universal set, write down the complements of the following sets:

$\{ x:x\, \ge \,7\} $