please take your time and show your steps and justification

4. (12 marks total) Let I = [0,1] and consider the following construction: remove the open interval (1/3,2/3) (the open middle third portion of I ) from I. This leaves us with the union of the two intervals [0, 1/3] and [2 / 3, 1]. Then, we remove the open mid- dle third from each of these intervals, resulting in the four intervals [0,1/9], [2 /9, 1 / 3], [2/3,7/Q], and [8/9, 1]. We repeat this process indenitely, removing the open middle third from every interval that remains from the preceding step. The set of all numbers in [0,1] that remain after all these open middle third intervals have been removed is called the Cantor ternary set, or simpl},r Cantor set, named after the German math- ematician George Cantor (1845-1918). A graphical representation of the construction of the Cantor set is shown below. (a) (b) (5 marks) Given an interval (cab) C R with a