. Show that if D(a,b) and D(b,c) have the same parity (i.e., are both even or are both odd), then D(a,c) must be even.
. Show that if D(a,b) and D(b,c) have the same parity (i.e., are both even or are both odd), then D(a,c) must be even.
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter12: Angle Relationships And Transformations
Section12.5: Reflections And Symmetry
Problem 20E
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For the cube graph , the distance between two vertices
a=(a1,a2,...,an) and b=(b1,b2,...,bn)
is called the “Hamming distance.” This is the number of positions where a and b differ. For instance, the Hamming distance between (0,0,1,0) and (1,1,0,0) is 3 because these two vertices differ in three positions. In each of the parts A,B below, D(x,y) is the Hamming distance in Qn:
A. Show that if D(a,b) and D(b,c) have the same parity (i.e., are both even or are both odd), then D(a,c) must be even.
B. Show that if D(a,b) and D(b,c) have different parity, then D(a,c) must be odd.
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