Here I am trying to show that the pair of Finite Automata are equivalent. I have tried something but I am not sure if I am in the right direction. This is what I have.
These are pairs of FA's. Set theory formula in here is
(L1' + L2)' + (L2' + L2)'
Both machines (FA1'+FA2)' and (FA2+FA1)' has no final states. (FA1'+FA2)' to have a final state, the machine (FA1'+FA2)' must have no final state. The exact same thing half of the formula. Clearly, if we added these machines together we would get a machine with nine state and no final state. Because there is no final state, it accepts no words and two languages L1 and L2 ar equivalent.
So the two regular expressions defame the same language and equivalent.
Am I in the right direction ?