d) Let P(x), Q(x), and R(x) be the statements "x is a professor," "x is ignorant," and "x is vain," respectively. Express each of these statements in symbolic form using quantifiers; logical connectives; and P(x). Q(x), and R(x), where the domain consists of all people. i. No professors are ignorant. i1. All ignorant people are vain. iii. No professors are vain. iv. There is a professor who is vain v. Some ignorant people are not vain vi. Prof. Agbotui is both ignorant and vain [1 mark] [1 mark] [1 mark] [1 mark] [1 mark] [2 marks] e) Let A(x), C(x), S(x) and GP(x) be the statements "x is an animal," "x is a cat,* "x is small," and "x is a good pet," respectively. Express each of these quantifications in English where the universe consists of all animals. [1 mark] [1 mark] [1 mark] [1 mark] i. Vx (C(*) ()) -3x(C(x) A-S(x)) 11. Vx (C(x) S(x) A A(x)) Vx (S(x) A A(x) - GP(x)) 111. iv.