11. Ada, Bea, and Clara have different characteristics. Exactly two are artistic; exactly two are beautiful; exactly two are intelligent; and exactly two are rich. Each has at most three characteristics. If Ada is intelligent, then she is also rich. Of Bea and Clara, it is true that, if she is beautiful, then she is artistic. Of Ada and Clara it is true that, if she is rich, then she is artistic. a. Define a set of propositional variables which encode whether a woman has a given characteristic. For example, AA might represent the proposition that Ada is artistic. How many variables are needed? Use the variables from part a. to provide a propositional formula that represents the statement "exactly two women are artistic" Use the variables from part a. to provide a propositional formula that represents the statement "Ada has at most three characteristics" Use the variables from part a. to provide a propositional formula that represents the statement "if Clara is rich, then she is artistic" b. c. d