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1-to evade a question
2-invite an obvious question
3-to ask a question that in itself makes unwarranted assumptions.
The quick and dirty tip is to remember that when something begs the question, it begs the question: what is your support for that premise?
*Begging the question is a logical fallacy in which a conclusion is based on an assumption that is as much in need of proof as the premise. Because that phrase is out there, and because many people are unfamiliar with the fallacy, beg the question is widely used to mean raise the question. This use of beg the question is a common peeve among people who care about English usage, but the phenomenon is so widespread that we should probably just accept that begging the question has multiple meanings.