Subspaces and Bases - Vectors

Question

In regards to the question, im confused because M is saying y is greater than x and positive, and N is saying that x is greater than y but is negative, so the union of the sets would be what? Any help is greatly appreciated

Answer 1

Try to do draw a picture and it's became easy

$[1,1]\in M$ and $[0,-2]\in N$ the summ of this two vectors are not in $P$