Let \(L(R)\) be the language represented by regular expression \(R\). Let…

Let $L(R)$ be the language represented by regular expression $R$. Let $L(G)$ be the language generated by a context free grammar $G$. Let $L(M)$ be the language accepted by a Turing machine $M$. Which of the following decision problems are undecidable?

I.    Given a regular expression $R$ and a string $w$, is $w \in L(R)$?

II.   Given a context-free grammar $G$, is $L(G) = \emptyset$

III.  Given a context-free grammar $G$, is $L(G) = \Sigma^*$ for some alphabet $Σ$ ?

IV.  Given a Turing machine $M$ and a string $w$, is $w \in L(M)$?