Product in finite state automata

Given below are two finite state automata (→ indicates the start state and F indicates a final state)Which of the following represents the product automaton Z×Y? GATECS200849

Antonio Anastasio Bruto da @antonio
20 Jan 2017 12:42 pm

I do not believe any of these options is correct. In both cases, observe that for automaton Y and Z on a (b) from the start state (1) they both go to the final state (2). Therefore in the product this will happen too. Using just this, we see that the only possible option is option (A) in which state (P) on a (b) goes to state (R), the final state. However (P) on an (a) goes to (S) , whereas (S) on an (a) should go back to (P) which doesn't happen. So the only feasible answer seems incorrect too.