5. Let M (S,+, L) be a model where S = {S0, S1, S2, S3}. The relation is {So + So, Si So, S2 + So, S2 + S1, S2 + S3, S3 + S2}. Furthermore, L(So) = {a}, L(SI) = 0, L(S2) = {0}, L(S3) = {a,b}. (a) Draw the state diagram for the model M. (b) Unwind the system to a depth of 4 starting from S2 (you may count the depth of first node as 1). (c) For each of the following formula o, identify an infinite path starting from S2 which satisfies # F . If such a path does not exist, then mention "does not exist. Justify your answer i. (OUX-6) A Xa ii. 6A ((XXX-a) Ua)