Need some help with a discrete Math logic problem A mathemat

Need some help with a \"discrete Math\" logic problem:

A mathematician tells her son, \"I will give you $100 only if you pass the class.\" Being a mathematician, she means exactly what she said.

Which ones below are the true statements about this situation?

a. If she didn\'t pay him $100, that means he didn\'t pass the class.

b. Her statement defined passing the class as a sufficient condition for receiving the $100.

c. If he passes the class, she may pay him $100.

d. Her statement defined passing the class as a necessary condition for receiving the $100.

e. If she ended up paying him $100, he must have passed the class.

f. If he passes the class, she will pay him $100.

g. He will not get the $100 unless he passes the class.

h. If he doesn\'t pass the class, she will definitely not pay him $100.

Solution

I will give you $100 only if you pass the class.

In this statement there is condition that \"only if\" you pass the class then I\'ll pay you.

True statements are:- (b) Her statement defined passing the class as a sufficient condition for receiving the $100.

(f) If he passes the class, she will pay him $100.

(g) He will not get the $100 unless he passes the class.

(h) If he doesn\'t pass the class, she will definitely not pay him $100.