Let $\backslash$Sigma $=\{0,1\}.$ Let us call two strings of same length to be distance $1$ apart if they $3$pts

differ in exactly one symbol. For example, for the string w $=101,$ the strings that

are distance $1$ apart from it are: $001,111,100.$ Consider the following operation on

languages:

Edit$1($A$)=\{$w $|$ there exists a string v in A such that v and w are distance $1$ apart$\}.$

Prove that the class P of languages is closed under the operation Edit$1.$