For each of the following statements, state whether it is True or False. (1) If \( L_1 \) and \( L_2 \) are regular languages, then \( L_1 \, \otimes \, L_2 = \{w : w \in (L_1 - L_2) \, \text{or} \, w \in (L_2 - L_1)\} \) is regular.- ○ True- ○ False

Answered: (1) If L₁ and L₂ are regular languages,…

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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For each of the following statements, state whether it is True or False.

(1) If \( L_1 \) and \( L_2 \) are regular languages, then \( L_1 \, \otimes \, L_2 = \{w : w \in (L_1 - L_2) \, \text{or} \, w \in (L_2 - L_1)\} \) is regular.

- ○ True
- ○ False

Expert Solution

Step 1: Step 1

The statement is false. The union of two regular languages is guaranteed to be regular, but the set you're describing, L1 ? L2, is not necessarily regular because it involves set differences (subtractions), which can lead to non-regular languages.

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