(a) Let V be the set of all ordered pairs (x, y) of real numbers, together with the nonstandard vector addition operation : V x V → V and standard scalar multiplication operation : Rx V → V given by: (x1, y₁) (x2, Y2) = (x₁ + x₂ + 1, y₁ + y2 + 1) k (x, y) = (kx, ky) Is V = (V,B,.) a vector space? Determine which of the vector space axioms V0-V4 and S0-S4 are satisfied, and which (if any) aren't.

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