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

- A
$A$

- B
$B$

- C
$\phi $

- D
$A \cap {B^c}$

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

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

$\varnothing^ {\prime}\cap A$

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

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

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 $\} $

If $U =\{1,2,3,4,5,6,7,8,9\}, A =\{2,4,6,8\}$ and $B =\{2,3,5,7\} .$ Verify that

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