Question

# The contrapositive of the statement 'If I am not feeling well, then I will go to the doctor' is${\text{A}}{\text{.}}$ If I am feeling well, then I will not go to the doctor${\text{B}}{\text{.}}$ If I will go to the doctor, then I am feeling well${\text{C}}{\text{.}}$ If I will not go to the doctor, then I am feeling well${\text{D}}{\text{.}}$If I will go to the doctor, then I am not feeling well

Hint: In order to solve this problem we need to know that the contrapositive is the statement, which is the opposite of the given statement. Also, the contrapositive of a statement is the switching of the hypothesis and the conclusion of a conditional statement and negating both.

Complete step-by-step solution:
Here the statement is 'If I am not feeling well, then I will go to the doctor'.
Let P be “I am not feeling well” and Q is “I will go to the doctor”.
Statements mean if P, then Q can be written as $P \to Q$
Now contrapositive of the statement is
$\Rightarrow \sim \left( {P \to Q} \right) = \sim Q \to \sim P$ (Since the contrapositive of P and Q is $\sim Q$ and $\sim P$)
This is written in statement as:
If I do not go to the doctor, then I am feeling well.
Hence option C is the correct answer.

Note: Here in this question the law of contraposition says that a statement is true if, and only if, its contrapositive is true. To form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement. The contrapositive of "If it rains, then they cancel school" is "If they do not cancel school, then it does not rain." If p, then q. If q, then p. And for solving these types of questions let the statement in symbol then apply contrapositive law to make the problem easy. Doing this will solve your problem and will give you the right answer.