Consider the following sets:

(a) A = {(x1, x2) R 2 : |x1| + |x2| 1};

(b) B = {x R 3 : 0 x1 x2 x3};

(c) C = {x R 2 : x2 (x1)2};

(d) (Bonus question) D = {(x1, x2, x3) R 3 : p x 2 1 + x 2 2 x3};

Q1a For each set, check if it is convex.

Q1b For each set, check if it is a cone.

Q1c Determine the extreme points of each convex.

Q1d Determine the recession cone of each convex set.

Support all answers by arguments