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Past exam of the mathematics course of the University of Cambridge / 2024 / ia / Paper 4 / 7E / b / iii / Solution

No, even when every element of

S

is positive. Take

S = {\frac{1}{2}}, T = {1, 2} .

Then

S^{T} = {1/2, 1/4}

, so

sup (S^{T}) = \frac{1}{2}, (sup S)^{s u p T} = (\frac{1}{2})^{2} = \frac{1}{4} .

Solved by gpt-5.6-sol high.

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