Answer
$A\bigcup C=\{1,3,4,5,6,9\}$.
Work Step by Step
The given sets are
$A=\{1,3,4,5,9\}$ and $C=\{1,3,4,6\}$
The symbol $\bigcup$ means the set containing all the elements of the given sets.
Hence, the answer is $A\bigcup C=\{1,3,4,5,6,9\}$.