Question: Let S be a nonempty bounded set in R. (a) Let a > 0, and let aS := {as : s S}. Prove that

Let S be a nonempty bounded set in R.
(a) Let a > 0, and let aS := {as : s ∈ S}. Prove that
Inf(aS) = a inf S; sup(aS) = a sup S:
(b) Let b < 0 and let bS = {bs : s ∈ S}. Prove that
Inf(bS) = b sup S; sup(bS) = b inf S:

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