4. (18 points) Prove or disprove each of the following statements: (Suggestions: 0 Please first state whether you think the statement is true or false. 0 If you decide to provide a example/counterexample, prove that your example sat- isfies all the required conditions.) (3) There does not exist a nonempty subset A of irrational numbers such that supA = 8 and ian = 6. (b) There exists a monotone sequence {5%} such that it contains a convergent subse quence but {1%} is itself divergent. (c) Let {33\"} be a sequence of positive real numbers. If {33\"} has no convergent subse quence, then {122\"} diverge to positive infinity. (Hint: You may use the fact that a subsequence of a subsequence is a subsequence of the original sequence.)