Question

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

• A. If I will catch the train, then I reach the station in time.
• B. If I do not reach the station in time, then I will catch the train.
• C. If I do not reach the station in time, then I will not catch the train.
• D. If I will not catch the train, then I do not reach the station in time.

Answer 1

The correct option is D

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

Finding the contrapositive of the given statement:

Given “If I reach the station in time, then I will catch the train”

$p$: I reach the station in time

$q$: I will catch the train

The given statement is of the form $p\to q$

Now the contrapositive of two statements will be

$$\begin{gathered} ~\left(p\to q\right) \\ \Rightarrow ~q\to ~p \end{gathered}$$

$~q$: I will not catch the train

$~p$: I do not reach the station in time

So, the statement becomes,

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

Hence, option (D) is the correct answer