6) [20 marks total] Consider the domain of people and the following argument: Hypothesis: - If a person is a mathematician, then he/she is a programmer. - If a person is a programmer, then he/she is prone to headaches. Conclusion: - Therefore, if a person is a mathematician, then he/she is prone to headaches. 1. [10 marks] Assign letters to the basic propositions and write each hypothesis and the conclusion as an implication. Hint: Use the syntax P(X): " X>0 " or P(X) : "subject and predicate" to represent your statements. 2. [10 marks] Prove the correctness of you answer to item a. by using the logical equivalencies and/or rules of inferences tables from your text which are also available below