Problem 7. (a) E Represent the set {x = (x₁, x₂) = R² | x12 ≥ 1}, as the intersection of some family of halfspaces. Take nonempty bounded set SCR". Prove that cl conv S = conv cl S. (b)

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A: As per bartleby guidelines we do only first three subparts and rest part can be reposted separately.

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A: We can find the answers as below.

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A: According to the given information, it is required to show that:

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Q: (a) Represent the set {x = (x1, x2) = R² | x1x2 ≥ 1}, as the intersection of some family of…

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A: Solution: