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### What is the regular languages that are equivalent to the given regular language: (0 + 1)*1(0 + 1)*

From: Athens View: 2312 qwerty1s

## Question

The target language is `(0+1)*1(0+1)*`. The choices are:

``````A) (01+11)*(0+1)*
B) (0+1)*(10+11+1)(0+1)*
C) (1+0)*1(1+0)*
D) (0+1)*(0+1)(0+1)*
``````

Multiple choices are allowed, if there's more than one equivalent language.

Consider your options, and either factor them into a form that looks like your target, or find a word that is in one language but not the other:

Target: `(0+1)*1(0+1)*`, this is the language of all words over `{0,1}` containing at least one `1`.

A) `(01+11)*(0+1)*`, this does not include at least one `1`. For example, the empty string is in A but not in the target.

B) `(0+1)*(10+11+1)(0+1)*`, looking specifically at the `10+11+1` part, which can be factored into `1(0+1+ε)`. `(0+1+ε)(0+1)*` is not different from `(0+1)*`.

C) `(1+0)*1(1+0)*`, this is just the target with `0+1` replaced with `1+0`. The union operation `+` is commutative.

D) `(0+1)*(0+1)(0+1)*`, this language includes the word `0` which is not in the target.