Express each of these statements using predicates and quantifiers [closed]

Question

Here is a problem from Kenneth Rosen's Discrete Mathematics and its Applications, Section 1.4

Express each of these statements using predicates and quantifiers.

A student must take at least 60 course hours, or at least 45-course hours and write a master’s thesis, and receive a grade no lower than a B in all required courses, to receive a master’s degree

The solution of Rosen for this problem was:

M→((H(60) ∨ (H(45) ∧ T)) ∧ ∀yG(B,y)), where Mis the proposition ''The student received a masters degree," H(x) is "The student took at least x course hours," T is the proposition "The student wrote a thesis," and G(x, y) is "The person got grade x or higher in his course y"

I am really confused with Rosen solution for this problem as it will be true if the student achieved all the requirements to receive the master degree however he will not receive it as: F → T ≡ T

Answer 1

As an English (or English-logic) statement, the sentence is consistent with the possibility that one does all the aforementioned things without actually receiving a degree. Whether or not those conditions are sufficient to receive a degree, in addition to being necessary, is just not within the scenarios encompassed by the sentence.

However, you should be warned that a great number of insitutions do not automatically award a degree to every student that meets those requirements because, for instance, the student might need to make a presentation of the thesis (which is evaluated), or the student should be alive by a certain date.