GPS$1\mathrm{.}8.$ Identify Cases

Create a regular expression for the language of all binary strings

such that

and

contains exactly one $1.$

The goal of this series of questions is to guide you through one possible approach to solving this problem. This is not the only approach, and we are not trying to suggest that it is the best approach.

The next step is to build regular expressions for each of the cases you identified in the previous part. With this step, we will have successfully converted the language intersection into a language union $("$and$"->"$or$").$

From the previous part, we know that the language accepts:

Strings in the form

where

and

$.$

Strings in the form

where

and

$.$

Strings in the form

where

and

$.$

Give a regular expression for strings in the form

where

and

$.$

regular expression

Give a regular expression for strings in the form

where

and

$.$

regular expression

Give a regular expression for strings in the form

where

and

$.$