Let S be a nonempty bounded subset of ℝ and let k ϵ ℝ. Define kS = {ks : s ϵ S}. Prove the following:
(a) If k > 0, then sup (kS) = k ∙ sup S and inf (kS) = k ∙ inf S.
(b) If k<0, then sup (kS) = k ∙ inf S and inf (kS) = k ∙ sup S.
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