#Theoryofcomputation #regularexpressions

Question

A = aa* and B = bb*

( A U B) * =?

1.{ a^nb^n | n >= 0}

2.{ a^mb^n | m, n >=0}

3.(a+b)*

4.None

Answer 1

A=aa* = $a^{+}$ = set of all strings of a's with one or more a

B= bb*=$b^{+}$ = set of all strings of b's with one or more b

we know that,

If R1 and R2 are regular expressions, then R1 | R2 (also written as R1 U R2 or R1 + R2) is also a regular expression.

so (AUB)*=( $a^{+}$ + $b^{+}$)*  =(a+b)*

 

so option 3 is correct.

Comments

That is what I am thinking.

if someone finds any counter example saying they are not equal then kindly inform so that I can correct it if any mistake i did.

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Hii,

I just want to know how did you type kleene plus in this, I  am unable to type any Superscript in this.

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use functions symbol at the header or google how to write superscript in latex.

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if A=a+

and B=b+

(A U B)*= (a^+ U b^+)* => (a U b)*

so option C is correct.

sorry for writing in this way I am not able to use superscript.