Let M = {(x,y) ∈ R^2 ∣ 0 ≤ x ≤ y}, N = {(x,y) ∈ R^2 ∣ 0 ≥ x ≥ y} and P = M ∪ N. P is closed under scalar multiplication. Give two vectors in P whose sum is not in P

Answer 1

Can you think of any more examples? Hope this helps! :)