Question

Draw appropriate Venn diagram for each of the following:
$\left(i\right)(A\cup B{)}^{\prime }$
$\left(ii\right)A^{\prime }\cap B^{\prime }$
$\left(iii\right)(A\cap B{)}^{\prime }$
$\left(iv\right)A^{\prime }\cup B^{\prime }$

Answer 1

$\left(i\right)$ Step $1:$ Draw $U,A$ and $B$

Step $2:$ Mark $A\cup B$

Step $3:$ Mark $(A\cup B{)}^{\prime }$, i.e., all region expect $(A\cup B)$.

$\therefore$ The orange region is $(A\cup B{)}^{\prime }$

$\left(ii\right)$ We know that, $A^{\prime }\cap B^{\prime }=(A\cup B{)}^{\prime }$ (By De-Morgan's law)


$\left(iii\right)$ Step $1:$ Draw $U,A$ and $B$

Step $2:$ Mark $A\cap B$

Step $3:$ Mark $(A\cap B{)}^{\prime }$ i.e., all region expect $(A\cap B)$

$\therefore$ The orange region is $(A\cap B{)}^{\prime }$

$\left(iv\right)$ We know that, $A^{\prime }\cup B^{\prime }=(A\cap B{)}^{\prime }$ (By De-Morgan's law)

$\therefore$ The orange region is $A^{\prime }\cup B^{\prime }$.