Which statement is logically equivalent to: "Make your payments on time and you will not receive a late fee."?

Question

If you do not receive a late fee, then you made your payments on time.

 

  It is false that if you make your payments on time, then you will receive a late fee.

 

  If you make your payments on time, then you will not receive a late fee.

 

  If you receive a late fee, then you did not make your payments on time.

Answer 1

the inverse proposition is

if you did not make your payments on time, you do not get a late fee

original proposition if P then Q

inverse if ~P, then ~Q

converse if Q then P

contrapostivie: if ~Q then ~ P