A mathematician tells her son, \"I will give you $100 only if you pass the class

Question

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.

Explanation / Answer

The true statements about this situation are :

a. If she didn't pay him $100, that means he didn't pass the class.
d. Her statement defined passing the class as a necessary condition for receiving the $100.
f. If he passes the class, she will pay him $100.
h. If he doesn't pass the class, she will definitely not pay him $100.

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