John's literature professor believes that the ability to judge the greatness of literary works accurately can be acquired only after years of specialized training.
Belief
Without years don't have ability to judge of specialized → greatness of literary training works
Facts
Without years can't become of specialized → a literature training professor
vast reading no access to years of majority of public specialized training
Evaluate
All three claims have this "years of specialized training" as an overlapping idea. Do the conditionals chain together?
No, but if someone doesn't have the specialized training, we'll know two things about them - can't be a literature professor - don't have ability to judge greatness of lit works
(A trap answer is probably going to try to make some conditional or over-quantified relationship between those two ideas)
Since we're told that most of the reading public doesn't have access to this training, we can infer two things ...
Goal
... Let's look for what we get when we apply the two conditional rules to the fact in the last sentence:
Vast majority of the reading public can't be a literature professor. Vast majority of the reading public can't judge the greatness of literary works.