Question 4 thank you

4. (10 points) Let P(x) be the statement "r has pet a unicorn", and let S(x, y) be the statement "r and y have shared a pizza", where the domain for the variables z and y consists of all students in the class. Express the following statements in predicate logic (a) Alice has shared a pizza with everyone except Carol. b) Everyone in the class who has pet a unicorn has shared a pizza with at least one other student in the class. (c) There are two students in the class who have not shared a pizza with anyone. (d) There are two students in the class who between them have shared a pizza with everyone else in the class. (e) If everyone in the class shares a pizza with someone, then no one pets a unicorn