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33 votes
33 votes

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
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5 Answers

Best answer
52 votes
52 votes
$I_1$ 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.
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26 votes
26 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 

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7 votes
7 votes

No, the inference 'I' is not Correct.

Let P = it rains.

Q = Cricket match will not be played.

For P $\rightarrow$ Q to be true.

If P is true then Q has to be true. (There is no other choice for Q).

But if P is false then Q can be anything (True or False). Still P $\rightarrow$ Q is true.

This is also known as "The fallacy of denying the antecedent".

P $\rightarrow$ Q
~P

$\therefore$ (Nothing can be concluded).

Answer:

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