Prove or disprove that, for any regular expressions R and S, (R*S*)* = (R + S)*
Prove or disprove that, for any regular expressions R and S, (R*S*)* = (R + S)*
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Question
Prove or disprove that, for any regular expressions R and S, (R*S*)* = (R + S)*
Expert Solution

Step 1
Answer:
Proof:
(R+S)* = (R*+S)*
= R*(R+S)*
= (R+SR*)*
= (R*S*)*
( OR)
-> R,S belongs to R*S*
(R*S*)* = (R+S+R*S*)*
(R+S+R*S*)* = (R+S)*
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