answer in detail

Problem 5. Suppose that A, = (-1, 1) is an open interval of real numbers between -1 and 1, for some n = 1, 2,..., 00. (i) Show that the union " A,, of all such intervals is open. [5 marks] (ii) Show that the intersection ()" A,, of all such intervals is not open. (5 marks] Next, suppose that B,. = [1, co) is the set of real numbers that are greater or equal to 1, for some n = 1, 2, ...,00. (iii) Show that the intersection ~B., of all such sets is closed. (5 marks] (iv) Show that the union ., B., of all such sets is not closed. (5 marks]