For the real-life arguments (i)-(x), write down the name of the law of reasoning that you believe occurs, whether you agree with the statements made or not: Modus Ponens, Modus Tollens, Disjunctive/Conjunctive addition, Conjunctive Simplification, Disjunctive/Hypothetical syllogism. Explain your process of thinking: assign propositional symbols to parts of the sentences, like we did in the first slide pack of the year with the example with Mr. Jenkins, and explain how those predicates encode the inputs and outputs of the rules. For some of the sentences, there might be more than one rule that could be applicable, depending on how you structure your answer! (i) Since I have both oranges and apples, it's true that I have apples. _________ (ii) If I studied, I would have passed 250. However, I did not pass, which means that I did not study._______ (iii) All men are mortal. Socrates is a man. Therefore, Socrates is mortal. _____ (iv) All CS UMD graduates become developers, and developers make good money. Therefore, all CS UMD graduates make good money. ________ (v) You wanted either a donut or an apple fritter, and they were out of apple fritters. So here's your donut. ______ (vi) Harry is my dog, and all dogs love bones. So I'm expecting him to love this bone. ______ (vii) I have experience in Android development, so I should respond to this job ad targeted to experienced Android or iPhone developers. ______ (viii) Beer upsets my stomach, and so does rum. So it doesn't matter which of the two I drink: I will still have an upset stomach. ________ (ix) Jacques is French and French people drink a lot of red wine. It follows that Jacques drinks a lot of red wine. (x) For Kathy, it was either that job or her mental health. Since she was fired from the job, she can look towards her mental health. ________ For example, suppose that we have the following argument: Everybody who drank the water was poisoned. Since Rita wasn't poisoned, she could not have drunk the water. If we encode drinks-water with p and gets poisoned with q, the first sentence can be encoded as p rightwardsdoublearrow q. We know that Rita wasn't poisoned, so ~q is also a given. The conclusion made is that Rita could not have drunk the water, so in terms of our encoding the conclusion is ~p. This is an application of modus tollens. You must show your work in the space provided to you below