This is a question from GATE CSE 2009.
Which of the following is FALSE?
A] There is a unique minimal DFA for every regular language.
B] Every NFA can be converted to an equivalent PDA.
C] Complement of every context-free language is recursive.
D] Every non-deterministic PDA can be converted to an equivalent deterministic PDA.
The answer provided to me (without any explanation) is B, which I think is wrong.
Here is my approach.
A] Every RL has an equivalent DFA and there is one unique minimal DFA for a given RL. [so True]
B] Since RL are proper sub-set of CFL and every RL has equivalent FA and every CFL has equivalent PDA, every FA can be converted to PDA but not vice versa. [so True]
C] Given a CFL we can create an equivalent Total TM [RECURSIVE], RECURSIVE languages are closed under complement. [so True]
D] This is only remaining option and by method of elimination answer.
Is my answer correct?