A minor supporting detail is "Books have been challenged and then banned from schools and libraries for many reasons: profane language, sexual or violent content, and religious or political views."
Reasons, illustrations, facts, procedures, or other types of proof that clarify the core notion are considered supporting details. The fundamental notion is developed and explained by major details. The minor details serve to clarify the important details.
The paragraph's main topic is about banning of books and the above mentioned statement states the reasons of banning books, which makes the sentence a minor supporting detail which is explaining the main topic.
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