Answer;
Deductive reasoning.
The above is an example of deductive reasoning because true statements (premises) are leading to a true conclusion.
Explanation;
The sentence contains the following premises that are true and precise:
1. "The entire drama team is going to the dance."
2. "Henry is on the drama team"
These premises in turn, lead to a true and logical conclusion, "Therefore, Henry is going to the dance."
The author is Guy de Maupassant
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I'm not too sure what you mean by "verxing ideas" -- perhaps it's a typo? But taking that out of the picture, the answer should be
a) strange ideas
Depend on who you're trying to persuade. Depending on the subject, the audience may be different, so the need for persuasion may have a different appeal. If it's a tragic novel, it may call for emotional and ethical persuasion. In a murder mystery, for example, it may call for logical and rational persuasion. In a fiction novel, it may call for facts and evidence, especially if evidence is needed to be cited. And most often times, persuasion includes interests and opinions, so don't worry about that one.