Recall that a set of propositional formulas is consistent if there is a truth assignment to each of the propositional variables that makes all propositional formulas simultaneously true. Is the following set of propositions consistent? Justify your answer by converting each statement to an equivalent logic statement. If consistent, give a suitable truth assignment that shows consistency. If not consistent, give a truth table to show that no truth assignment simultaneously satisfies all formulas. 1. A dog that is brown or fluffy is a good dog. 2. If a dog loves treats then they are a good dog. 3. Fluffy white dogs don't like treats. 4. Every dog is fluffy or loves treats or is a good dog. 5. A dog which does not likes treats and is not fluffy is a bad dog