$[15$ pts$]$ If an algorithm $A$ is in the complexity class $P,$ is it also necessarily in the complexity class

NP$?$ Explain why or why not.

$[15$ pts$]$ Given an alphabet $=\{a,b,c\},$ list all strings from length $2$ to $4$ in the language

$L=b(a+b)**c,$ Assume the empty string $$ is length $0.$

$[15$ pts$]$ Draw a state transition diagram for the FA of regular language $L(r)$ where

$r=b^{**}aa(a+b)**$