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**spring** how can we determine the following sets are convex or not? can it be enough to draw a 3d graph? or how can we apply the formula f($\displaystyle \alpha$x + (1-$\displaystyle \alpha$)y) $\displaystyle \leq$ $\displaystyle \alpha$f(x) + (1-$\displaystyle \alpha$)f(y) for f(x1,x2)?

Which of the following sets are convex and which are not?

a. {(x1 x2) : x1^2+ x2^2 $\displaystyle \leq$ 1}

b. {(x1, x2) : x1 = 1, |x2| $\displaystyle \leq$ 4)

c. {(x1, x2) : x2 — x1^2 = 0}

d. {(0,0), (0,1), (1,0), (1,1)}