Suppose I have two LL languages $L_1, L_2$, both describable by LL($k$) grammars for the same $k$, and regular language $R$. Which of the following are also LL languages, and can they be described by LL($k$) grammars?

- $L_1 cup L_2$ (union)
- $L_1 circ L_2$ (concatenation)
- $L_1^*$ (Kleene star)
- $L_1 cap R$ (intersection with a regular language)