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Convex Sets

Give an example in R2 of a convex set. (I know that an example of a convex set is something like a circle or something just as long as you can draw a segment between and 2 pts and the segment still be in the circle, I think, I know something like the packman shape or a peanut is NOT convex)

Anyway my teacher wants the answer is the form {(x,y):??????} I don't know how to put it into that form.

Also if you can I'm having the same problem for giving an example of a connected set in R2 in the same form.

Solution Summary

An example in R2 of a convex set is provided. The solution is detailed and well presented.