# GATE CSE 2009, Which of the following is FALSE?

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.