1. The mechanic knew either the oil filter was clogged or the oil pump was defective. He just replaced the oil filter. If he has replaced the oil filter, then he knew the oil pump is defective. Therefore, he knew the oil pump is defective. a. By representing the propositional variable appropriately, list down the hypothesis and conclusion into the mathematical form. [7 marks] b. Determine the appropriate rules of inference to be used to deduct the hypotheses in order to get the conclusion. [10 marks] By using the truth table, show that the conjunction of the listed hypotheses implies the conclusion (e.g., H H2^H3 C) is a tautology. [8 marks] C.