Given below are two statements:

Statement I: The problem "Is $L_1\cap L_2=\phi$?" is undecidable for context sensitive languages $L_1$ and $L_2$.

Statement II: The problem "Is $W\in L$?" is decidable for context sensitive language $L$, where $W$ is a string.

In the light of the above statements, choose the correct answer from the options given below:

Statement I is true.

For context sensitive languages, the emptiness problem is undecidable.

Since context sensitive languages are closed under intersection, checking whether:

$L_1\cap L_2=\phi$

is also undecidable.

So, Statement I is true.

Statement II is also true.

Membership problem for context sensitive languages is decidable.

This is because context sensitive languages are accepted by Linear Bounded Automata, and for a fixed input there are only finitely many configurations.

Therefore, we can decide whether $W\in L$ or not.

So, both statements are true.