1. Let n E N and suppose X is a set with n elements. Define V as the set of all functions f : X → C. The set V together operations + and . described below (f + g)(x) = f(x) + g(x) VxEX, (c. f)(x) = c f(x) Vc E C and Vx EX forms a vector space. Find a basis of the vector space V.

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