Pikuai answers~
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A writer writes puns for humor or levity.
While often time un-funny, puns are used to add humor or a lighter tone/mood to the story.
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The option that describes a homophonic pun is a pun that uses two words that look the same but have different meanings
The word homophonic is based/comes from music, by music I mean the way some notes may look the same but sound different.
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Hope this helps, have a amazing day!~