1. (10 points) Give the traces on the set of atomic propositions {a,b} of the following transition system. 2. (10 points) Consider the set AP ={A,B} of atomic propositions. Formulate the following properties as LT properties and characterize each of them as being either an invariance, safety property, or liveness property, or none of these. (a) A should never occur, (b) A should occur exactly once, (c) A and B alternate infinitely often, (d) A should eventually be followed by B. 3. (10 points) Consider the following transition system TS with the set of atomic propositions {a}: Consider the fairness assumption to be: F=(,{{},{}},{{}}) Determine whether TS=F "eventually a". Justify your