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Assume x, y and z are n bit binary numbers then which of the following inequalities hold about Hamming Distance between them?

A. HD(x,y)+HD(y,z)>=HD(x,z)

B. HD(x,y)+HD(y,z)<=HD(x,z)

C. HD(x,y) - HD(y,z)>=HD(x,z)

D. None of the above

1 Answer

Best answer
4 4 votes

A)

It is correct. 

If y lies between x and z then H(x,y) + H(y,z) =H(x,z)

If y doesnt lie betwween x and z then H(x,y) + H(y,z) > H(x,z) 

B)

It is wrong since we have proved A) is correct

C)

If x and y are equal then LHS will be negative. So it is also wrong

Hence answer should be A)

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