Question

Consider the following two statements :

I. If all states of an NFA are accepting states then the language accepted by the NFA is ${\sum }^{\ast }$.

II. There exists a regular language A such that for all languages B, $A\cap B$ is regular.

Which one of the following is CORRECT?

Answer 1

I. Incorrect, since even if all states of NFA are accepting, dead configuration may be there and L need not be ${\sum }^{\ast }$.

II. Correct, since $\varphi$ is regular and $\varphi \cap B=\varphi$ which is regular for all B.