Which of the following arguments are not 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. Codes: (A) (a) and (c) (B) (b) and (c) (C) (a), (b) and (c) (D) (a) and (b)

Which of the following arguments are not 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.

Codes:

(A) (a) and (c) (B) (b) and (c) (C) (a), (b) and (c) (D) (a) and (b)
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1 Answer

Answer :

Answer: B

Explanation:

(a) P: Gora gets the job

 Q: Gora works hard

 R: Gora gets promotion

 S: Gora will be happy

The argument can bet written as

 (P˄Q)→R

 R→S

 ¬S

 Therefore ¬P˅¬Q


(b) Let P: Puneet is not guilty

 Q: Pankaj is telling the truth

The argument can bet written as

 P˅Q

 ~Q

 Therefore, P

Thus by disjunctive syllogism, the argument is valid.

Disjunctive Syllogism:

The disjunctive syllogism rule may be written as:

P˅Q, ¬P ⊢Q

It may also be written as:

((P˅Q)˄¬P)→Q

where P, and Q are propositions expressed in some formal system.


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