Let's consider words over the alphabet {a,b} to be sequences of a and b with finite length. We say u≤v if u is a subword of v if we can get u erasing some letter of v (for example aba≤abbab). We say that u differentiates the words x and y if u≤x but u≤y or vice versa.Let m and l be positive integers. We say that two words are m−equivalents if there does not exist some u with length smaller than m that differentiates x and y.a) Show that, if 2m≤l, there exists two distinct words with length l \ m−equivalents.
b) Show that, if 2m>l, any two distinct words with length l aren't m−equivalent. Combinatorics of wordscombinatoricsmath olympiad