The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
x
+18 votes
1k 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 Veteran (14.6k points)
edited by | 1k views

2 Answers

+29 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 (332k points)
selected by
This is an example of Modus tollen. Isn't it ?
yes it is example of modus tollens

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

+8 votes

Let us assume p=It rains,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 an inferenece.

I2:can be written as 

p->q

 ~p


~q

Not an inference.

Hence answer is B 

answered by Boss (8.5k points)
Nice detailed answer .....


Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true

32,330 questions
39,146 answers
108,244 comments
36,501 users