Question 4 (a) (b) (0} Employ a truth table to determine if the following argument is valid. (~33) V 1" (premise) (~r) H q (premise) q > (w) (premise) (q V r) A (~39) (conclusion) (7 marks} Use the rules of inference in propositional logic to show that the following argument form is valid. (3) > {3) V 1" (premise) (~q) A (~S) (premise) u > S (premise) a V p (premise) p A \"r (conclusion) (8 marks} Let P(x, 3;) denote the predicate: x will attend school on Day 3). Let 0(2) denote the predicate: There is home-based learning on Day 2. Let R(w) denote the predicate: Day W is the eve of a holiday. Let 5(17) denote the predicate: Day 1.? is the middle of the work week. Express the following argument using the predicates P(x, 3)), 0(2), R (MILE (1?) as well as logical connectives, and identify any logical fallacies that are present. Premise A: If Day w is either the even of a holiday or the middle of the work week, then there is home-based learning on Day w. Premise B: 2-Nov-2022 in the middle of the work week. Premise C: Janice will not attend school on Day y only if there is home-based learning on Day 3;. Conclusion: Janice will not attend school on 2-Nov-2022. (5 marks}