Let (X, || ||x) and (Y, ||- ||y) be the normed spaces. Let XOY := {(x, y): xe X;y ≤ Y} denote the direct sum of X and Y. For each element (x, y) E XY, put ||(x, y)||₁ := ||||x+||yl|y. (a) Show that || ||₁ is a norm function on XY. . (b) Show that if X and Y both are Banach spaces then the space X Y under the norm || ||1 is also a Banach space.

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