Consider the following sets:
a. A = {(x₁, x₂) ∈ R : |x₁| + |x₂| ≤ 1};
b. B ={x ∈ R³: 0 ≤ x₁ ≤ x₂ ≤ x₃}
c. C = {x ∈ R² : x₂ ≤ x²₁};
d. D = {(x₁, x₂, x₃) ∈ R³: √(x²₁ + x²₂) ≤ x₃};
For each set:
1. prove or disprove it is convex.
2. prove or disprove it is a cone.
3. determine the extreme points (if convex).
4. determine the recession cone (if convex).