Please help me with this two homework questions, for each question, only choose 1 option and explain why, thanks!

1. Suppose a language L is context free. Then what we can say about the following two languages?

i) L ( L L )

ii) L ( L L )

A) The first language must be context free; where the second language may not be context free.

B) The first language may not be context free; where the second language must be context free.

C) Both languages are context free.

D) Both languages are not context free.

E) We can't judge base on the information given.

2.

Is the following correct?

To convert a DFA into an equivalent PDA, replace every transition in the transition diagram of the DFA by a transition between the same pair of states in the PDA while not pushing or popping characters from the stack.

A.It is correct because DFAs are a type of PDAs that ignore the stack.

B. It is not correct because PDAs do not have transition diagrams.

C.It is correct because DFAs and PDAs recognize the same class of languages.

D.It is not correct because there is a regular language that is not recognized by a PDA.