If $A$ and $B$ are two given sets, then $A \cap {(A \cap B)^c}$ is equal to

Draw appropriate Venn diagram for each of the following:

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

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

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

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

$\{ x:x$ is an even natural number $\} $

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\} $

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

$B^{\prime}$