Q45,. Which of the following regular expression identities are true ?

(A) (r + s)* = r* s*

(B) (r + s)* = r* + s*

(C) (r + s)* = (r*s*)*

(D) r* s* = r* + s*

Answer©

Explanation.

Let take string” rrssrs”

Take + as either one of the path and * as the loop either 0 or more times.

Option (A)  (r + s)* = r* s*

left side  may be

While()

{

Either r or s

};

Left side realize the string. Where as right side fails to realize the string. Because r* s*=

While()

{r}

While()

{s}.

Option (B) (r + s)* = r* + s*

Left side realize the string where as r* + s* =

If()

{

while()

{r

}

Else

{

while()

{s}

}

So right side fails to realize the string “rrssrs”.

Option (C)    (r + s)* = (r*s*)* .

While()

{

While()

{

R

}

While()

{

S

}

}

Right side also realize the string. Hence the answer.