MAT 243 HW3 - MAT 243 HW 2 Jile Shi 1.6 14 b Let r(x ber is...

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MAT 243, HW 2, Jile Shi 1.6 14 b) Let r(x) be “r is one of the five roommates listed,” Let d(x) be “x has taken a course in discretemathematics,” Let a(x) be “x can take a course in algorithms.” Y: represents an arbitrary person. x(r(x) d(x)) Hypothesis r(y) → d(y) 1Universal instantiation x(d(x) a(x)) Hypothesis d(y) → a(y) , 3Universal instantiation r(y) → a(y) 2,4 Hypothetical syllogism x(r(x) a(x)) 5 Universal generalization 16: a) Let p(x) be the proposition ”x is enrolled in the university.” Let q(x) be the proposition ”x has lived in a dormitory.” x(p(x) q(x)) Premise p(Mia) q(Mia) Universal instantiation ¬q(Mia) Premise. ¬p(Mia) The argument is valid. b) Let P(x) be ”x is a convertible car.” Let Q(x) be ”x is fun to drive.”
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This argument is invalid because we cannot get ¬ Q(Isaac ’s car ) from x(P(x) Q(x)), and ¬P(Isaac’s car). c) It ’s incorrect. d) Let P(x) be ”x is a lobsterman.” Let Q(x) be ”x set at least dozen traps.” x(P(x) Q(x))
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  • Spring '06
  • Callahan
  • Math, Rational number, Irrational number, universal instantiation, nonzero rational number

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