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Question 57

The contrapositive of the statement "If I reach the station in time, then I will catch the train" is:

First, we identify the logical form of the given English sentence. The sentence “If I reach the station in time, then I will catch the train” can be written in symbolic logic as $$P \rightarrow Q,$$ where

$$P : \text{“I reach the station in time,”}$$ $$Q : \text{“I will catch the train.”}$$

Now, we recall the definition of a contrapositive. For any implication of the form

$$P \rightarrow Q,$$

the contrapositive is obtained by simultaneously negating both parts and reversing their order. Symbolically, the contrapositive is

$$\neg Q \;\rightarrow\; \neg P.$$

Here $$\neg$$ (read “not”) is the logical negation operator. So we proceed step by step.

First we negate the consequent $$Q$$: $$\neg Q : \text{“I will not catch the train.”}$$

Next we negate the antecedent $$P$$: $$\neg P : \text{“I do not reach the station in time.”}$$

Finally, we reverse their order in the implication. Thus the contrapositive of $$P \rightarrow Q$$ is written in words as

“If I will not catch the train, then I do not reach the station in time.”

This matches exactly with Option D.

Hence, the correct answer is Option D.

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