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well-defined sets are sets that can identify easily while not well-defined are those that cannot determined easily :)
Yes, the set of happy people is not well defined.
Real world problems are basically about stuff you do every day, but put into a question when doing boring math work. Now, if you're wanting to know about life itself, well that's like war and what not. Stuff that stresses you out, that's what real world problems are. :(
If there exists even one single item for which you cannot say whether it is in the set or not, the set is not well defined.
Yes, they ARE.