If $A=\{3,5,7,9\}, B=\{1,3,5\}, \mu =\{1,2,3,4,5,7,9\}$ then $(A\cup B)\text{'}=$

The union of two sets is a set, having all the elements of both sets

Hence, $A\cup B=\{1,3,5,7,9\}$

The complement of a set $A$ is $A\text{'}=\mu -A$

Hence, 

$\begin{array}{rcl}\left(A\cup B\right)\text{'}& =& \mu -\left(A\cup B\right)\\ & =& \left\{1,2,3,4,5,7,9\right\}-\{1,3,5,7,9\}\\ & =& \{2,4\}\end{array}$

Therefore, $\begin{array}{rcl}\left(A\cup B\right)\text{'}& =& \boxed{\{2,4\}}\end{array}$