Question

Let R₁​ and R₂​ be regular expressions. From the list below, select all statements that are necessarily true.

A) R₁+R₂ ​ is also a regular expression.
B) R₁+R₂ is also a regular expression.
C) R₁​ is also a regular expression.
D) ¬R₁ ​ is also a regular expression.

Answer 1

The statements A) R₁+R₂ ​ is also a regular expression and B) R₁+R₂ is also a regular expression are true.

Step-by-step explanation:

The correct statements are A) R₁+R₂ ​ is also a regular expression and B) R₁+R₂ is also a regular expression.

To understand why these statements are true, we need to know that regular expressions can be combined using operators such as + (union), concatenation, and * (Kleene star). When we take the union of two regular expressions, R₁ and R₂, we get a new regular expression, R₁+R₂, which represents the language that contains all the strings that can be generated by either R₁ or R₂.

For example, if R₁ represents the language of all strings containing the letter 'a' and R₂ represents the language of all strings containing the letter 'b', then R₁+R₂ represents the language of all strings that can contain either 'a' or 'b'.