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Let $N(f) =$ the class of languages accepted by Non- deterministic Finite Automata,
$N(p) =$  the class of languages accepted by Non- deterministic Push down Automata,
$D(f)=$ the class of languages accepted by Deterministic Finite Automata; and,
$D(p)=$ the class of languages accepted by  Deterministic Push down Automata.

Then, which one among these statements is TRUE?

  1. $D(f)$ subset of $N(f)$ and $D(p)$ subset of $N(p)$
  2. $D(f)$ subset of $N(f)$ and $D(p) = N(p)$
  3. $D(f) = N(f)$ and $D(p) = N(p)$
  4. $D(f) = N(f)$ and $D(p)$ subset of $N(p)$
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D is correct answer!
NFA and DFA accept the same class of language(Regular) hence both have same powers.
While DPDA accepts the proper subset(DCFL) of the language accepted by NPDA(CFL).

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i am confused with proper subset and subset in perticular question which are suitable ,in question written as subset is it purely correct or not????
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