Consider the following sets:
(a) A = {(x₁, x₂) ∈ R²: ∣x₁∣ + ∣x₂∣ ≤ 1};
(b) B = {x ∈ R³: 0 ≤ x₁ ≤ x₂ ≤ x₃}; Hint: Recall {x:Ax ≤ 0} is a convex cone;
(c) C = {x ∈ R²: x₂ ≤ x₁²};
(d) D = {(x₁,x₂,x₃) ∈ R³: √x₁² + x₂² ≤ x₃};
For each set:
1. Prove or dispose it is convex