Q$2.$ Consider the state diagram below: a$)$ Fill in the state transition table b$)$ Suppose that there are three primitive propositions $($p$,$q$,$r$)$ associated with the state machine with their truth values in the various states given below Find the interpretation functions I$($p$),$ I$($q$),$ I$($r$)$ on these propositions c$)$ Suppose there are two observers Bar and Foo. Both have faulty knowledge. When machine is in state A$,$ Bar believes it to be in state D and vice$-$versa. Foo believes that machine is in state C when it is actually in state B$.$ It perceives the other three states correctly. Find J$($Bar$)$ and J$($Foo