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

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 $(A \cup B)^{\prime}=A^{\prime} \cap B^{\prime}$

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

$(B-C)^{\prime}$

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

${{\mathop{\rm U}\nolimits} ^\prime } \cap A =  \ldots $

Draw appropriate Venn diagram for each of the following:

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

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

$\{ x:x$ is a perfect cube $\} $