The contrapositive of the statement

Question:

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

  1. If I will catch the train, then I reach the station in time.

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

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

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


Correct Option: , 3

Solution:

Let $\mathrm{p}$ denotes statement

$\mathrm{p}$ : I reach the station in time.

q: I will catch the train.

Contrapositive of $\mathrm{p} \rightarrow \mathrm{q}$

is $\sim \mathrm{q} \rightarrow \sim \mathrm{p}$

$\sim \mathrm{q} \rightarrow \sim \mathrm{p}:$ I will not catch the train, then $\mathrm{I}$ do not reach the station in time.

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