Which of the following arguments are valid? (a) "If Gora gets the job and…
2015
Which of the following arguments are valid?
(a) "If Gora gets the job and works hard, then he will be promoted. if Gora gets promotion, then he will be happy. He will not be happy, therefore, either he will not get the job or he will not work hard."
(b) "Either Puneet is not guilty or Pankaj is telling the truth. Pankaj is not telling the truth, therefore, Puneet is not guilty."
(c) If 𝑛 is a real number such that 𝑛 > 1, then 𝑛2 > 1. Suppose that 𝑛2 > 1, then 𝑛 > 1.
- A.
(a) and (c)
- B.
(b) and (c)
- C.
(a), (b) and (c)
- D.
(a) and (b)
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Correct answer: D
Final conclusion: Only the argument that infers n > 1 from n^2 > 1 is invalid; the other two arguments are valid.
Gora argument: From "If Gora gets the job and works hard, then he will be promoted" and "If he is promoted then he will be happy", take contrapositives: not happy implies not promoted, and not promoted implies either not getting the job or not working hard. Composing these gives not happy implies (not getting the job or not working hard), so the conclusion follows and the argument is valid.
Puneet/Pankaj argument: From the disjunction "Puneet is not guilty or Pankaj is telling the truth" together with the fact that Pankaj is not telling the truth, conclude that Puneet is not guilty by disjunctive syllogism. Therefore this argument is valid.
Numeric argument: The step from n^2 > 1 to n > 1 is not valid in general because a negative number with absolute value greater than 1 also has square greater than 1. For example, n = -2 gives n^2 = 4 > 1 while n > 1 is false. Thus this argument is invalid.
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