Problem 2 [15 points] For each of statements below, either find a model that does not satisfy it, or prove it is valid. Important Note. You need to first translate each statement into a propositional or predicate formula, and then show whether the formula is valid or not. (a) (5 points) If there is a pandemic, a highly transmissible virus exists, and if a highly transmissible virus exists then I am infected. Either there is no pandemic, or no highly transmissible virus exists. Therefore, either no highly transmissible virus exists or I am infected. (b) (5 points) Some students have taken a formal method course and some students have taken software testing. Therefore some students have taken a formal method course and software testing course. (c) (5 points) Every employee who has asked for a raise has not received a raise. Someone has received a raise. Therefore, some employee has not asked for a raise