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

1 1/4 hours

step-by-step explanation:

2/4 + 2/4 + 1/4 = 5/4 or 1 1/4

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.