Let $M$ be the language of all binary strings that contain the substring $11$ and whose

number of $0\text{'}$s is even. $($For example, $0101100$ is in M$.)$ Answer the following with

justification:

$($a$)$ Give a collection of strings such that your strings are pairwise distinguishable with

respect to $M$ and your collection is as big as possible.

$($b$)$ Give a collection of strings such that your strings are pairwise indistinguishable

with respect to $M$ and your collection is as big as possible.