conclusion. [Some logic texts call this the fallacy of affirmingthe consequent.](b) Why is reasoning using this argument form deemed invalid?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)j(Frodo)(∀x)(j(x)→h(x))∴(∃x)(c(x)∧h(x))Proof of validity:1.(∀x)(j(x)→h(x)): Hypothesis2.j(Frodo)→h(Frodo) : 1,Universal Instantiation3.j(Frodo): Hypothesis4.h(Frodo): 2,3,Modus Ponens5.c(Frodo): Hypothesis6.c(Frodo)∧h(Frodo): 5,4,Conjunction7.(∃x)(c(x)∧h(x)): 6,Existential Generalization
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