Some pure math

This problem is solved using simple set theory and knowledge of union and intersection of sets. Union of two sets, $X$ and $Y$ , i.e., $X\cup Y$ is defined as the set consisting of all the elements of $X$ and $Y$ while intersection of two sets $X$ and $Y$ denotes the set consisting of all those elements which are common to both $X$ and $Y$ .

Now, given here that --> $X=\{3,4,7,18\} ,\quad Y=\{4,7,16,19\}, \quad Z=\{16,18,19\}$

Then, we have, $X\cup Y = \{3,4,7,18\}\cup \{4,7,16,19\}=\{3,4,7,16,18,19\}$

Now, we further have, $(X\cup Y)\cap Z = \{3,4,7,16,18,19\}\cap \{16,18,19\} = \boxed{\{16,18,19\}}$

(X (union) Y) is 3, 4, 7, 16, 18, 19. That set all the values in this set are in Z, so the intersection is the same as the set Z (16, 18, 19).