Recursive Definitions

$1.$ Give a recursive definition for the set B of bitstrings which contain arbitrary number of

$0$ bits but contain exactly one bit $1.$

$2.$ Give a recursive definition for the set B of bitstrings which contain arbitrary number

of $0$s and $1$s$,$ but don$$t contain substring $11,$ i$.$e$.$ they do not contain a run of two

consecutive $1$s$.$

$3.$ Give a recursive definition for the set B of bitstrings which contain arbitrary number

of $0$s and $1$s$,$ but don$$t contain substring $111,$ i$.$e$.$ they do not contain a run of three

consecutive $1$s$.$