Using these propositional constants, encode the following English sentences as sentences in propositional logic.
Purple mushrooms are poisonous.
A mushroom is poisonous only if it is purple. A mushroom is not poisonous unless it is purple. For each sentence below, determine whether it is valid, satisfiable but not valid, or unsatisfiable. You may use truth tables, proofs by hand, Logica, or Otter. Each subproblem is worth two points.