Let F denote some finite language, R denote some regular language, C denote some context-free language, D denote some decidable language, E denote some recognizable language, and N denote some non-recognizable language. For each of the following statements, prove whether it always holds, sometimes holds, or never holds:

a) RN is regular Holds: always / sometimes / never proof:

b) N - R is regular Holds: always / sometimes / never proof:

c) N (opposite sign of U) F is not regular Holds: always / sometimes / never proof:

d) N - F is regular Holds: always / sometimes / never proof:

e) C* is infinite Holds: always / sometimes / never proof:

f) R is context- free Holds: always / sometimes / never proof: