Please answer the question in the picture below. Please show accurate steps clearly.

1. Dene the fat Cantor set S as follows: Beginning with [0,1], remove the middle quarter open interim! frorn it to obtain r 1 = [l], %] U [3, l]. Inductively given St, remove from each elosmi interval comprising 3;, the middle open interval subinterval having length 3% to obtain 3*\". Then, we let S = 3\". n=1 {21) Write out the union of closed intervals that comprises 82. 2". + 1 22n+l ' (b) Show inductively that the length of each elm-mi :suhiuterw in 8,; thunk; (e) Prim: that MS) = %