Propositional Puzzle $(10$ points$)$: Write out the facts as sentences in Propositional Logic, and use propositional resolution to solve the crime. $1.$ There are three suspects for a murder: Adams, Brown, and Clark. $2.$ Adams says $$I didn$$t do it$.$ The victim was an old acquaintance of Brown$$s$.$ But Clark hated him.$3.$ Brown states $$I didn$$t do it$.$ I didn$$t know the guy. Besides, I was out of town all week.$4.$ Clark says $$I didn$$t do it$.$ I saw both Adams and Brown downtown with the victim that day; one of them must have done it$.5.$ Assume that the two innocent men are telling the truth, but that the guilty man might not be$.$