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+22 votes
1.6k views

Consider the following logical inferences.

$I_{1}$: If it rains then the cricket match will not be played.
The cricket match was played.
Inference:  There was no rain.

$I_{2}$: If it rains then the cricket match will not be played.
It did not rain.
Inference: The cricket match was played.

Which of the following is TRUE?

  1. Both $I_{1}$ and $I_{2}$ are correct inferences
  2. $I_{1}$ is correct but $I_{2}$ is not a correct inference
  3. $I_{1}$ is not correct but $I_{2}$ is a correct inference
  4. Both $I_{1}$ and $I_{2}$ are not correct inferences
asked in Mathematical Logic by Boss (18.3k points)
edited by | 1.6k views

3 Answers

+33 votes
Best answer
$I_1$ is a correct inference. $I_2$ is not a correct inference as it was not mentioned what would have happened if it hadn't rained- They might have played or they might not have played.
answered by Veteran (359k points)
selected by
+2
This is an example of Modus tollen. Isn't it ?
+1
yes it is example of modus tollens
0

Only I1 is example of Modus Tollen. I2 does not look like Modus Tollen. Pooja Palod mam. please confirm. 

0

I2 is an example of Logical Fallacy.Usually fallacy occurs in two forms:

Form 1)The Fallacy of affirming the consequence

If p then q.  AND
q

Then we cannot conclude anything.

Form 2) The fallacy of denying the antecedent.

If p then q.  AND

NOT P

Then we cannot conclude anything.

 

+13 votes

Let us assume p=It rains, the q=cricket match will not be played.

I1: If it rains then the cricket match will not be played   (p->q)

The cricket match was played. (~q)
Inference:  There was no rain.(~p)

p->q

~q


~p    (Modus tollens )

Thus I1 is a correct inference.

I2: can be written as 

p->q   
 ~p


Given inference - ~q 
Not a correct inference. When p is false and q is true, both the premises becomes true but conclusion becomes false

Hence answer is B 

answered by Loyal (8k points)
edited by
0
Nice detailed answer .....
+1

I2 is a famous Fallacy.
This type of incorrect reasoning is known as Fallacy of denying the hypothesis.

Another one is -
p->q
q


p
It is known as Fallacy of affirming the conclusion.  


 

+4 votes

B) I1 is correct but I2 is not a correct inference.

answered by Boss (23.9k points)


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