Need some help with a \"discrete Math\" logic problem: A mathematician tells her

ID: 3405596 • Letter: N

Question

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.

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.

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