Question

What is the contrapositive of the following: "If I form a study group then I raise my grades." A. If I work alone then I lower my grades. B. If I raise my grades then I form a study group. C. If I lower my grades then I work alone D. If I form a study group then I lower my grades. E. If I form a study group then I raise my grades. F. If I raise my grades then I work alone.

Answer 1

Answer:

C. If I lower my grades then I work alone

Step-by-step explanation:

In logic, the contrapositive of a conditional statement, $P\to Q$ is $\neg Q\to \neg P$.

In other words, the contrapositive of "If P then Q" is "If not Q, then not P".

The given conditional statement is:

"If I form a study group then I raise my grades."

We can break this conditional statement into the following propositional statements:

P : I form a study group

¬P : I work alone

Q : I raise my grades

¬Q : I lower my grades

The contrapositive of  "If I form a study group then I raise my grades." becomes:

" If I lower my grades then I work alone"

The correct choice is C