We defined our regular expression language on page 12, lecture 2. The language contains the operators * and +. We can eliminate r* from our language without reducing its expressiveness since r* has the same semantics as (r^+|epsilon). Can we eliminate r^+ from our language without reducing its expressiveness by using a semantically equivalent regular expression that uses r*? If yes, give the semantically equivalent regular expression. Can we eliminate both, r* and r^+, from the language without reducing the expressiveness? If yes, give the semantically equivalent regular expressions for the eliminated operators.Show transcribed image text We defined our regular expression language on page 12, lecture 2. The language contains the operators * and +. We can eliminate r* from our language without reducing its expressiveness since r* has the same semantics as (r^+|epsilon). Can we eliminate r^+ from our language without reducing its expressiveness by using a semantically equivalent regular expression that uses r*? If yes, give the semantically equivalent regular expression. Can we eliminate both, r* and r^+, from the language without reducing the expressiveness? If yes, give the semantically equivalent regular expressions for the eliminated operators.