Answer
$A\bigcup B=\{1,2,3,4,5,6,7,8,9\}$.
Work Step by Step
The given sets are
$A=\{1,3,4,5,9\}$ and $B=\{2,4,6,7,8\}$
The symbol $\bigcup$ means the set containing all the elements of the given sets.
Hence, the answer is $A\bigcup B=\{1,2,3,4,5,6,7,8,9\}$.