Which of the following statements is logically equivalent to "if i study, then i get better grades"? if i do not study, then i do not get better grades. if i get better grades, then i study. if i do not get better grades, then i do not study. if i get better grades, then i do not study.

I would think that the correct answer is the 1st one: If I do not study, then I do not get a better grade. 

I think this would be correct because it's basically the same as the sentence they give you! For a better understanding of this, go to:   https://en.wikipedia.org/wiki/Logical_equivalence

I hope this helps you out!