Let $L_1$ be the recursive language. Let $L_2$ and $L_3$ be languages that are recursively enumerable but not recursive. Which of the following statements is not necessarily true?
- $L_2 - L_1 \:\text{is recursively enumerable.}$
- $L_1 - L_3 \:\text{is recursively enumerable.}$
- $L_2 \cap L_3 \:\text{is recursively enumerable.}$
- $L_2 \cup L_3 \:\text{is recursively enumerable.}$