Let P be a nondeterministic pushdown automaton (NPDA) with exactly one state, q, and exactly one symbol, Z, in its stack alphabet. State q is both the starting as well as the accepting state of the PDA. The stack is initialized with one Z before the start of the operation of the PDA. Let the input alphabet of the PDA be S. Let L(P) be the language accepted by the PDA by reading a string and reaching its accepting state. Let N(P) be the language accepted by the PDA by reading a string and emptying its stack.
Which of the following statement is TRUE?

L(P) is necessarily ∑* but N(P) is not necessarily ∑*

N(P) is necessarily ∑* but L(P) is not necessarily ∑*

Both L(P) and N(P) is necessarily ∑*

Neither L(P) nor N(P) are necessarily ∑*