Determine whether the set, together with the indicated operations, is a vector space. If it is not, then identify one of the ten vector space axioms that fails.

The set

{(x, y): x ? 0, y is a real number}

with the standard operations in R2

A) The set is a vector space. The set is not a vector space because it is not closed under addition.

B) The set is not a vector space because an additive identity does not exist.

C) The set is not a vector space because it is not closed under scalar multiplication.

D) The set is not a vector space because a scalar identity does not exist.