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)

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30 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**?

- Both $I_{1}$ and $I_{2}$ are correct inferences
- $I_{1}$ is correct but $I_{2}$ is not a correct inference
- $I_{1}$ is not correct but $I_{2}$ is a correct inference
- Both $I_{1}$ and $I_{2}$ are not correct inferences

0

47 votes

Best answer

Only I_{1} is example of Modus Tollen. I_{2} does not look like Modus Tollen. Pooja Palod mam. please confirm._{ }

0

25 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 **

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).**