Consider the following logical inferences. $\text{I}_1$: If it rains then the cricket match will not be played. The cricket match was played. $\textbf{Inference}$: There was no rain. $\text{I}_2$: If it rains then the cricket match will not be played. It did not rain. $\textbf{Inference}$: The cricket match was played. Which of the following is $\textbf{TRUE}$?

Let $p$ denote "It rains" and $q$ denote "The cricket match is played". The conditional statement is: "If it rains, then the cricket match will not be played", which translates to $p \to eg q$.

1. For Inference $\text{I}_1$:

   • Premise 1: $p \to

eg q$- Premise 2:$q$(The cricket match was played) - Inference:$ eg p$ (There was no rain)

By *Modus Tollens*, from $p \to eg q$ and the negation of the consequent $eg(eg q) \equiv q$, we can validly infer the negation of the antecedent$ eg p$. Thus,$$\text{I}$_1$ is a valid/correct inference.

2. For Inference $\text{I}_2$:

   • Premise 1: $p \to

eg q$- Premise 2:$ eg p$(It did not rain) - Inference:$q$ (The cricket match was played)

Inferring $q$ from $eg p$ is the fallacy of *Denying the Antecedent*. If it did not rain, the cricket match might or might not be played for other reasons. Thus, $\text{I}_2$ is not a correct inference.

Therefore, $\text{I}_1$ is correct but $\text{I}_2$ is not a correct inference, which corresponds to option (B).