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+21 votes
1.3k 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?
 
    (A) Both $I_{1}$ and $I_{2}$ are correct inferences
    (B) $I_{1}$ is correct but $I_{2}$ is not a correct inference
    (C) $I_{1}$ is not correct but $I_{2}$ is a correct inference
    (D) Both $I_{1}$ and $I_{2}$ are not correct inferences
asked in Mathematical Logic by Boss (18k points)
edited by | 1.3k views

3 Answers

+31 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 (342k points)
selected by
+2
This is an example of Modus tollen. Isn't it ?
0
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. 

+11 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 (7.9k points)
edited by
0
Nice detailed answer .....
0

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.  


 

0 votes

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

answered by Boss (12.7k points)


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