UGC NET CSE | December 2012 | Part 3 | Question: 45

Question

Which of the following regular expression identifies are true?

• A. (r+s)*=r*s*
• B. (r+s)*=r*+s*
• C. (r+s)*=(r*s*)*
• D. r*s*=r*+s*

Answer 1

Correct answer would be C) ${(r + s)}^{*}$ = ${(r^{*} s^{*})}^{*}$

Because you can generate all the string from RHS, which can be generated from LHS.

Comments

I was confuse in option B and C, why not option B is answer?

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Because $(a+b)$ means either you can choose $a$ or $b$ but not both. You can imagine it like its two path from A to B. You can choose any one of them but not both. 

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thanks