Let L be the set of all binary strings that contain a $1$ as the fourth symbol from the end of the string.

$($a$)$ Give an NFA to accept L$.$

$($b$)$ Use induction over the length of input strings to show that the given NFA accepts L$.$ To help in

the proof write claims about what each state in your NFA does and consider why a string of any

length may be in that and if the string would be accepted or not.