Are this statments true or false: It is unknown whether P and NP are actually the same class.

Two grammars generating the same language may not be equivalent.

Only certain relation symbols have arity.

G$$del$\text{'}$s Incompleteness Theorem states that number theory is undecidable.

All the NP$-$complete languages are also EXPTIME$-$complete languages.

For computable functions, there can be Turing Machines that do not halt

The set of rational numbers is uncountably infinite.

A Finite State Machine is defined by a $6-$tuple.

In regular expressions star and union operators bind tighter than the concatenation operator.

Computation of a deterministic Turing Machine can be shown on a tree in contrast to computation of a Nondeterministic Turing Machine.

Axioms require proofs of their statements.

Turing Machines and Lambda Calculus are not equivalent in power.

Turing Machines can move the head over the tape by more than one cell at each step of their operation.

Regular expressions are not equivalent with regular languages.

There are no languages which would not be Turing recognizable.

Pumping lemma for regular languages cannot be used to prove that certain languages are not regular.

In the Chomsky Hierarchy type$-3$ languages are regular, type$-2$ languages

are context$-$sensitive$,$ type$-1$ languages are context$-$free, while type$-0$ languages are recursively enumerated.

The Halting Problem for a Turing Machine is decidable.

All languages are Turing recognizable.

Adding nondeterminism to Turing Machines makes them non$-$equivalent to Deterministic Tms$.$

There exist different variations of Turing Machines definitions which are not equivalent.

For any transformation function on Turing Machines there will never exist a Turing Machine which would be unchanged by the transformation.

Not every regular language is context free.

A regular expression cannot be defined using recursion.

Regular languages are not equivalent with Finite State Machines.

Equivalence between variations of Turing Machines can be understood in terms of computing efficiency.

If P and NP classes would be the same it doesn't necessarily mean that

for all problems in the NP class there would exist polynomial time solutions.

There exist questions about regular languages that are not decidable.

Not every context$-$free language is known to be in P$.$

Turing recognizable languages form a subset of decidable languages.

Every context$-$free language is in the P complexity class.

Not every problem about regular languages is decidable.

The set of all languages is uncountably infinite.

A language is context$-$free if for example there exists a Pushdown Automaton that recognizes it$,$ but also in other cases.

A language is in NP if it is decided by some Nondeterministic Polynomial$-$Time Turing Machine, as well as in other cases.

The P complexity class is either a subset of the PSPACE class or both classes are the same.

All different variations of Turing Machines are equivalent in computing capability.