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