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Write each of the following arguments in argument form (i.e., using propositions, predicates, quantifiers, and logical operators). Then, use the rules of inference to prove that each argument is valid. You must indicate the name of the rule used in each step of the proof
A.) Let c be “I am in Chicago,” n be “I am in New York,” g be “I am in Germany,” ℎ be “I will get a hot dog,” and m be “I will get some mustard.”
If I am in New York, then I won’t get a hot dog. I am in New York or Chicago. I will get some mustard and a hot dog. Therefore, I am in Chicago or Germany
B.) Let P(x) be “x purrs,” H(x) be “x is happy,” and G(x) be “x is hungry,” where the domain of x consists of all cats.
There is a cat that doesn’t purr. Every cat that is happy or hungry, purrs. Therefore, there is a cat that isn’t happy
C.) Let R(x) be “x runs,” E(x) be “x eats,” and S(x) be “x sleeps,” where the domain of x consists of all dogs.
Every dog runs or eats. Every dog that eats but doesn’t run, sleeps. Therefore, every dog that doesn’t sleep, runs.
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