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Which of the following arguments are not valid?

  1. "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." 
  2. "Either Puneet is not guilty or Pankaj is telling the truth. Pankaj is not telling the truth, therefore, Puneet is not guilty."
  3. If $n$ is a real number such that $n>1$, then $n^2 > 1$. Suppose that $n^2 > 1$, then $n>1$.
    1. i and iii
    2. ii and iii
    3. i,ii, and iii
    4. i and ii
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Ans→None of the above options

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,

_____________________________________________________________________

∴∴ either he will not get the job or he will not work hard.

[JOB Λ WH] → P

P → H

~H

_____________________________________________________________________

~JOB V ~WH

To check whether the given argument is valid or not, let’s assume that the conclusion is false because for a valid argument at least one premise should be false(I can’t make all premises true) If all sets of premises are true then it is an invalid argument else valid argument.

for the conclusion to be false; JOB = T ; WH = T

for 3rd premise, He will not be happy states that ~H is true here hence truth value of H is false

for 1st premise [JOB Λ WH] → P needs to be true we need to make P true as well

for 2nd premise P → H; P = T; H = F; T → F results in false. It’s not possible to make this premise true.

Hence all premises aren’t true here. Therefore, it is a valid argument.

b)  "Either Puneet is not guilty or Pankaj is telling the truth. Pankaj is not telling the truth, therefore, Puneet is not guilty."

~G V T

~T

____________________________________________________________________

~G

case of disjunctive syllogism. Hence, it is a valid argument.

c) If n is a real number such that n>1, then n2>1. Suppose that n2>1, then n>1

equivalent to 

If n is a real number such that n>1n>1, then n2>1

____________________________________________________________________________

Suppose that n2>1, then  n>1

 

≡ p→q

____________________________________________________________________________

 q→p

we know that by implication it isn’t true that if p→ q is true then q→p need not be true also.

hence, it is an invalid argument.

ans→None of the above options

 

 

 

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