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

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

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

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

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

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

If $U=\{a, b, c, d, e, f, g, h\},$ find the complements of the following sets:

$B=\{d, e, f, g\}$

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

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