Let I ⊂ R be a bounded and nonempty interval. Show that there are numbers a, b ∈ R with a ≤ b and I =[a,b] or I =[a,b) or I =(a,b] or I =(a,b)

Answer: I is nonempty real numbers bounded interval. It's bounded so, there will two real numbers a,b such a ≤ x ≤ b for all x in I. Since I is interval so , Either I=[a,b] if a,b are also elements of I Or, I=(a,b] if b is also elements of I Or, I=[a,b) if a is also elements of I Or, I=(a,b) if a,b is not elements of I Proved.