2. Let RE be the set of regular expressions over alphabet E = {0, 1}, and for r E RE, let L(r) be thelanguage denoted by r. Consider the claim:VL E P(E*),Vr1, r2 E RE, (|L(r1)| > 1 A L \ L(r2) = L(r1)) = L is regularEither prove this, or find L, rı and r2 that provide a counter-example.

2. Let RE be the set of regular expressions over alphabet E = {0, 1}, and for r E RE, let L(r) be the language denoted by r. Consider the claim: %3D VL E P(E*), Vr1, r2 E RE, (|L(r1)| > 1 ^ L \ L(r2) = L(r1)) = L is regular Either prove this, or find L, r1 and r2 that provide a counter-example.

2. Let RE be the set of regular expressions over alphabet E = {0, 1}, and for r E RE, let L(r) be the language denoted by r. Consider the claim: %3D VL E P(E*), Vr1, r2 E RE, (|L(r1)| > 1 ^ L \ L(r2) = L(r1)) = L is regular Either prove this, or find L, r1 and r2 that provide a counter-example.

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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2. Let RE be the set of regular expressions over alphabet E = {0, 1}, and for r E RE, let L(r) be the
language denoted by r. Consider the claim:
VL E P(E*),Vr1, r2 E RE, (|L(r1)| > 1 A L \ L(r2) = L(r1)) = L is regular
Either prove this, or find L, rı and r2 that provide a counter-example.

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