Undecidability

Consider the following sets:

S1: Set of all recursively enumerable languages over the alphabet {0, 1}.
S2: Set of all syntactically valid C programs.
S3: Set of all languages over the alphabet {0, 1}.
S4: Set of all non-regular languages over the alphabet {0, 1}.

Which of the above sets are uncountable?

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 Turning 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, L(G)=\phi?
III. Given a context-free grammar G, is L(G)=\Sigma* for some alphabet \Sigma?
IV. Given a Turning machine M and a string w, is w\inL(M)?

Which of the following decision problems are undecidable?
I. Given NFAs N1 and N2, is L(N1)\capL(N2) = \phi?
II. Given a CFG G = (N,\Sigma ,P,S) and a string x \in\Sigma ^*, does x \in L(G)?
III. Given CFGs G1 and G2, is L(G1) = L(G2)?
IV. Given a TM M, is L(M) = \phi?

Which one of the following problems is undecidable?

Let \Sigma be a finite non-empty alphabet and let 2^{\Sigma^{*}} be the power set of \Sigma^{*} . Which one of the following is TRUE?