You are given n envelopes, numbered 0; 1; : : : ; n 1. Envelope 0 contains 20 D 1 dollar, Envelope 1 contains 21 D 2 dollars, . . . , and Envelope n 1 contains 2n1 dollars. Let P. n/ be the assertion that: For all nonnegative integers k < 2n, there is a subset of the n envelopes whose contents total to exactly k dollars. Prove by induction that P. n/ holds for all integers n 1