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Convex Sets

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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.

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

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A circular area can be defined as the collection of points that are within distance R from the origin.

For a point (x,y) in Euclidian space, the distance to the origin r is:

So a circle is defined as all the points that satisfy

For example, ...

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