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This is my 4th Post All Questions Are Wrnh

Let us define the set P:={(x,y)RnRmTx+Wyr,y0}, where matrices T and W, and vector r are of appropriate dimensions. Let us also define the set S:={xRnyRms.t.(x,y)P} which is assumed to be nonempty, closed, convex. (a) (15 points) Suppose that x^/S. Argue that there exists an inequality, defined by a vector (,)Rn+1, such that x^