Since the proposition above is a contingency, one cannot beone hundred per cent certain that the truth of the conclusionfollows from the truth of the hypothesis. That, of course, isunacceptable behavior for a rule of inference, and is why werequire all the implications used as rules of inference to betautologies.[Think about betting your life on the rules ofinference!!]8. (15 pts.)c(Frodo)¬h(Frodo)(∀x)(j(x)→h(x))∴(∃x)(c(x)∧¬j(x))Proof of validity:1.¬h(Frodo): Hypothesis2.(∀x)(j(x)→h(x)): Hypothesis3.j(Frodo)→h(Frodo): 2,Universal Instantiation4.¬j(Frodo): 1,3,Modus Tollens5.c(Frodo): Hypothesis6.c(Frodo)∧¬j(Frodo) : 5,4,Conjunction7.(∃x)(c(x)∧¬j(x)): 6,Existential Generalization
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