model checking exercice explanation

Do the following properties hold in M? If yes, provide a brief justification, if no provide a counterexample path. (a) a. (b) a (c) ((a union c) a) For formula (1) in Question 1, write all the formal steps needed to show if every accepting run of A satisfies it. Express the following specification as LTL formula on the alphabet {p, d}, where p means that the button is pushed and d means that the process is currently deadlocked, and build the equivalent automaton: "Always, if the button is pushed, a certain process will eventually be permanently deadlocked