This is a very simple question.
Let's say there is $ Z_{1} \cup Z_{2} $
Where $ Z_{1} = \emptyset $ and $ Z_{2} $ = $ \left\{ x \mspace{4mu} | \mspace{4mu} x \in \mathbb{R},\mspace{4mu} 9<x \right\} $
Would $ Z_{1} \cup Z_{2} $ = $ \left\{ x \mspace{4mu}|\mspace{4mu} x = \emptyset \mspace{4mu}\mspace{4mu} or \mspace{4mu}\mspace{4mu}x \in \mathbb{R}, 9<x \right\} $
be equivalent to $ Z_{1} \cup Z_{2} $ = $ \left\{ x \mspace{4mu}| \mspace{4mu}\mspace{4mu}x \in \mathbb{R}, 9<x \right\} $ ?
I think it is, but I am not sure if the empty set is in the interval.
No, it's $\{x \mid x \in \emptyset \text{ or } x \in \mathbb{R}, 9 < x \}$. And the first clause is never true (there are no elements in the empty set!) so can be omitted.
So you are left with just $Z_2$ again.