Problems$1.$ Explicit state model checking. Consider a system, where we have states s$0,$ s$1,$ s$2,,$ s$9,$ s$10.$ Theinitial state is s$0$ only. There is a transition from a state si to si$+5,$ for all $0$i$5.$ Additionally, there aretransitions from si to si$-3,$ for all $3$i$10.$ For each state si we define an associated atomic predicate pi$.$That is$,$ p$0$ is true in s$0$ and nowhere else, p$1$ is true in s$1$ and nowhere else, $...,$ p$10$ is true in s$10$ andnowhere else.Using the explicit$-$state model checking algorithm presented in class, determine if the followingproperties hold.a$.$ EF p$1$b$.$ AF p$2$c$.$ AG $($ p$9->$ AF p$3)$d$.$ AG $($ p$4->$ EF p$10)$Note: Please submit a drawing of the Kripke Structure as part of your answer. Please note that youare NOT asked to simply answer the questions by looking at the Kripke Structure. You areasked to use the algorithm presented in class!