(a) [4 points) Let p and 9 and r be the following propositions: P: Bob passes this course. q: Bob does every assignment. T Bob takes the final exam. Write the following propositions using p, q, and r and negations and logical connectives: (₁) Bob passes this course, but he does not do every assignment. If Bob takes the final exam and does not do every assignment, then he does not pass this course. (iii) It is not the case that Bob either passes this course or takes the final exam. (iv) Bob takes the final exam if and only if he does every assignment. (b) [3 points] Let p, q and r be the following propositions: P: Kate is athletic. q: Kate likes skiing. r: Kate enjoys running. Express each of the following propositions as an English sentence: (1) 9 Ap (ii) T P P→ (9^r) (iii)