# Thread: are these sets are convex or not?

1. ## are these sets are convex or not?

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( $\alpha$x + (1- $\alpha$)y) $\leq$ $\alpha$f(x) + (1- $\alpha$)f(y) for f(x1,x2)?

Which of the following sets are convex and which are not?
a. {(x1 x2) : x1^2+ x2^2 $\leq$ 1}
b. {(x1, x2) : x1 = 1, |x2| $\leq$ 4)
c. {(x1, x2) : x2 — x1^2 = 0}
d. {(0,0), (0,1), (1,0), (1,1)}

2. Originally Posted by 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( $\alpha$x + (1- $\alpha$)y) $\leq$ $\alpha$f(x) + (1- $\alpha$)f(y) for f(x1,x2)?

Which of the following sets are convex and which are not?
a. {(x1 x2) : x1^2+ x2^2 $\leq$ 1}
b. {(x1, x2) : x1 = 1, |x2| $\leq$ 4)
c. {(x1, x2) : x2 — x1^2 = 0}
d. {(0,0), (0,1), (1,0), (1,1)}
What 3d graphs? Which function f? As far as I can tell you're asking about convex sets not convex functions, so to see that a set is convex you pick any two points x,y in the set and check that the segment tx+(1-t)y is in the set for all 0<t<1. For the first one it's easier to do if you know that intersection of convex sets is convex.