a. Yes, w={1,2,3,4,5,6} is contiguous in s.
b. Yes, both w={1,2,3,4} and w={3,4,5,6} are contiguous in s.
c. Yes, both w={1,2} and w={3,4,5,6} are contiguous in s.
d. No, w={1,2,3} is not contiguous in s, but both w={2,3,4,5} and w={4,5,6} are contiguous in s.
In order to determine whether each of the given subsequences (w) is a contiguous subsequence of the respective sequences (s), we need to examine the structure and arrangement of elements in each case.
a. s={1,2,3,4,5,6}
The subsequence w={1,2,3,4,5,6} is contiguous in s because it appears in the exact order without any elements missing or additional elements.
b. s={1,2,3,4}{1,2,3,4,5,6}{3,4,5,6}
The subsequence w={1,2,3,4} is contiguous in s since it appears in the beginning without interruption.
However, w={3,4,5,6} is also contiguous in s because it starts at index 9 and continues without any gaps.
c. s={1,2}{1,2,3,4}{3,4,5,6}{5,6}
Both w={1,2} and w={3,4,5,6} are contiguous in s as they appear without breaks or extra elements.
d. s={1,2,3}{2,3,4,5}{4,5,6}
The subsequence w={1,2,3} is not contiguous in s because there is a gap between the first and second sets.
The subsequences w={2,3,4,5} and w={4,5,6} are contiguous in s.