Hi,i have a automata hw could you help me

1. (100 pts) Consider a DFA with the following transition table FGE HCG Use the table filling algorithm to find all the pairs of distinguishable states and the equivalence classes. Show your work 2. For any language C, we define PAL(C) as follows For example, if C = {a, ab). then PAL(c)-(a, alba). 1. (50 pts) Prove that the regular languages are not closed under this operation 2. Given a DFA M-(Q, ,6,9. F) which recognizes some language L (you may ahesume $ ): (a) (150 pts) Describe a PDAF. (Q..r,8,4. F") that ncognize, PAL(C). b) (150 pts) Prove that C(P)- PAL(C