for
Section 6: Arguments and Proofs
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23. p true, q true
25. p true, q false, r false
27. Invalid. For a counterexample, we can take p = "1 = 1," q = "the moon is made of green cheese," and r = "2+2 = 4."
31. Invalid. This is the same argument as the one in (23). Note that, although the reasoning is incorrect, the conclusion is true. I don't eat grass.
41. Not necessarily; let sl = "switching speaker leads results in left channel failure," sr = "switching speaker leads results in right channel failure," cl = "switching CD leads results in left channel failure," cr = "switching CD leads results in right channel failure," fl = "fault with left speaker," fa = "fault with amplifier," and fc = "fault with CD player." Then a counterexample is given by taking fl, fa, fc, sl, sr, and cr all true, and cl false.
45. Valid
45. Invalid: Let y = "you glue," w = "Wu glues," g = "Golly glues," m = "Molly glues," s = "Solly glues," h = "Holly glues," d = "Dolly glues." For a counterexample, let y be F, w T, g F, m anything, s F, h T, and d anything.
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![]() | Stefan Waner (matszw@hofstra.edu) | ![]() | Steven R. Costenoble (matsrc@hofstra.edu) |