Let V = {(x, y) ∈ ℐ² : x, y > 0}. Define addition + of any two elements (x, y), (w, z) ∈ V by (x, y) + (w, z) = (xw, yz) where xw on the right-hand side denotes standard multiplication of the two real numbers x and w, and yz is interpreted similarly. Define scalar multiplication on V so that for all λ ∈ ℐ and (x, y) ∈ V we have λ(x, y) = (x^λ, y^λ) where x^λ on the right-hand side denotes the standard operation of raising a positive real number to the power of another real number, and similarly for y^λ. It can be verified that V is a vector space over the field of real numbers ℐ. Let W = {(x, y) ∈ V : x, y ≥ 1}. Which one of the following statements is true?
Select one:
a. W is closed under addition but not under scalar multiplication
b. W is closed under scalar multiplication but not under addition
c. W is not closed under either addition or scalar multiplication
d. W is a vector space, but not a subspace of V
e. W is a subspace of V
