10To prove the second part, let l j be the least integer such that r l j≥ 1/p j .Then p j ≥ r −l jand ∑ r −l jj ≤ ∑ j p j = 1. Thus the l j satisfy the Kraft-McMillan inequality and hence there is a prefix (sic) encoding f: A → C ∗with code lengths l 1 , … , l n . But l j < 1 − log 2 p j / log 2 (r), by E.**2.**2, andhence l = ∑ j p j l j< 1 + H/log 2 (r).E.**2.****2.** Show that the least integer such that r l j≥ 1/p j is− log 2 p j / log 2 (r).In particular, l j < 1 − log 2 p j / log 2 (r).E.**2.**3. Use the Kraft-McMillan inequality to show that the setC = {0, 01, 11, 101}is not a code and find a binary string that can be decomposed in two differentways as a concatenation of elements of C.