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.

C. If I lower my grades then I work alone

Step-by-step explanation:

In logic, the contrapositive of a conditional statement, is .

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

answer: can and shows the work

step-by-step explanation:

50 min

step-by-step explanation:

they will be decreasing both their times in half

60 / 2 = 30

40/2 = 20

30 + 20 = 50