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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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?

- $D(f)$ subset of $N(f)$ and $D(p)$ subset of $N(p)$
- $D(f)$ subset of $N(f)$ and $D(p) = N(p)$
- $D(f) = N(f)$ and $D(p) = N(p)$
- $D(f) = N(f)$ and $D(p)$ subset of $N(p)$

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