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