# GATE | GATE CS 2008 | Question 30

Let fsa and pda be two predicates such that fsa(x) means x is a finite state automaton, and pda(y) means that y is a pushdown automaton. Let equivalent be another predicate such that equivalent (a, b) means a and b are equivalent. Which of the following first order logic statements represents the following:

Each finite state automaton has an equivalent pushdown automaton.

(A) A
(B) B
(C) C
(D) D

Explanation: Considering each option :

(A) If everything is a FSA, then there exists an equivalent PDA for everything.

(B) It is not the case that for all y if there exist a FSA then it has an equivalent PDA.

(C) Everything is a FSA and has an equivalent PDA.

(D) Everything is a PDA and has exist an equivalent FSA.

Thus, option (A) is correct.

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