Consider the predicate logic language with three constants Mike, Bill, and John, and three relations Hits (x, y), Tall (x), and Alive (x). I show the variables after the relation name just to indicate how many arguments the relation expects. M1. Show a predicate logic model for this language. M2. How many predicate logic models are there for this language? M3. How many predicate logic models are there for this language if you consider only the domain {1}? M4. Let P be the formula Hits (Mike, John) and Q be the formula (\forall x) (\forall y) Hits (x, y). a. Does P entail Q? If not, show a predicate logic model that is a counter example. If so, expand the definition of "entails" to say what "P entails Q" means without using the word "entails". b. Does Q entail P? If not, show a predicate logic model that is a counter example. If so, expand the definition of "entails" to say what "Q entails P" means without using the word "entails