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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

Given: $R\rightarrow \ \sim C$

Hence: $C\rightarrow \ \sim R$

When it rains, we can imply there's no cricket match.

When it doesn't rain, we can' say anything. (because $\sim R$ doesn't imply anything)
I think it is first question added on Gateoverflow.
I1 is true due to “modus tollens” (or “rule of contrapositive”)

I2 is false because of “fallacy of assuming inverse”

So, option B is true.

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$I_1$ 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.
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.

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.

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

by

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.

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

edited
but ,

P -> Q

~Q

-----------------

This is possible right ?

~P

P $\rightarrow$ Q
~Q

$\therefore$   ~P

This is also known as Modus Tollen