If anyone could explain how the following problem is done, I would really appreciate it!

Here is a vector candidate. The set is R, and we define scalar multiplication by ax = a * x (usual scalar multiplication) and vector addition by x (insert circle symbol with plus sign in it that means vector addition) y = max(x, y).

For each of the following three vector space axioms, either verify the axiom or show that it does not hold.

a) a(x+y) = ax + ay

b) There exists an element 0 such that for any x in the proposed vector space, x + 0 = x.

c) x+y = y+x