Let X = Y = [0, 1] and f: X x Y R be defined by...

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Let X = Y = [0, 1] and f: X x Y→ R be defined by f(x,y) (a) For each xe X, find F(x) = sup{f(x, y): y = Y}; then find sup{F(x) : x = X}. (b) For each ye Y, find G(y) = sup{f(x, y): xe X}; then find sup{G(y): y = Y}. (c) Find sup{f(x, y) : (x, y) = X × Y}. Compare your answer with parts (a) and (b). = Let X = Y = [0, 1] and f: X x Y→ R be defined by f(x,y) (a) For each xe X, find F(x) = sup{f(x, y): y = Y}; then find sup{F(x) : x = X}. (b) For each ye Y, find G(y) = sup{f(x, y): xe X}; then find sup{G(y): y = Y}. (c) Find sup{f(x, y) : (x, y) = X × Y}. Compare your answer with parts (a) and (b). =

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