Question 2 (6 Points) Show that the following statements are inconsistent. That is, find a con- tradiction. i) If Sergei takes the job offer then he will get a signing bonus. ii) If Sergei takes the job offer then he will get a higher salary. iii) If Sergei gets a signing bonus, then he will not get a higher salary. iv) Sergei takes the job offer Question 3 (6 Points) Let C(x) be the statement "x has a cat." Let D(x) be the statement "x has a dog." Let F(x) be the statement "x has a ferret." Express each of these statements using quantifiers, predicates given, and logical connectives. The domain for the statements is all Computer Science students at UAB. a) A student in the department has a dog, a cat, and a ferret. b) All students in the department have a cat, a dog, and a ferret. c) Some student in the department has a dog, a cat, but no ferret. d) No student in the class has a dog, a cat, and a ferret. e) For each of the three animals there is a student in the department who has the animal as a pet