powerscore里关于sufficient condition, necessary condition的问题

行疆者思

If you get an A+, then you must have studied.
Taking the above statement as true, consider the following three statements:
1. John studied for the test, so he must have received an A+ on the test.
2. John did not receive an A+ on the test, so he must not have studied for the test.
3. John did not study for the test, so he must not have received an A+ on the test.
不知道第三句为什么对，我觉得原句只告诉我get an A+是must have studied的充分条件，并没有告诉我must have studied 是 get an A+的必要条件啊。
放上powersore里的解释：Statement 3 is valid. If studying is the necessary condition for getting an A+, and John didn’t study, then according to the original statement there is no way John could have received an A+. This inference is known as the contrapositive, and you can see that when the necessary condition fails to occur, then the sufficient condition cannot occur.
拜托大家教教我，感谢感谢