Prove that if A is a nonempty set which is bounded below by 3 then B = {x ∈ R | ∃a ∈ A, b = (1/a)} is bounded above by (1/3)

7. Let A and B be bounded nonempty subsets of R, and let A + B := {a+b : a € A, b € B}. Prove that sup(A + B) = sup A + sup B and inf(A + B) = inf A +inf B.

3. Let A = {a} be a bounded subset of R. Which of these three statements about A is/are not true? I: max A does not exist. II: sup A = infA III: min A< max A A I and II only в. П only C.I and III only D. I, II and III E. None of the above. 4.