**Problem Statement**(4) If \( L_1 \cup L_2 \) is a context-free language, then \( L_1 \) and \( L_2 \) must be context-free.**Options**- ○ True- ○ False**Explanation**This is a multiple-choice question related to context-free languages in theoretical computer science. The question investigates whether the union of two languages being context-free implies that each language independently must also be context-free.

Answered: (4) If L₁ U L₂ is a context free…

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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**Problem Statement**

(4) If \( L_1 \cup L_2 \) is a context-free language, then \( L_1 \) and \( L_2 \) must be context-free.

**Options**

- ○ True
- ○ False

**Explanation**

This is a multiple-choice question related to context-free languages in theoretical computer science. The question investigates whether the union of two languages being context-free implies that each language independently must also be context-free.

Expert Solution

Step 1: Introduction

In formal language theory, context-free languages play a significant role in describing the syntactic structure of many programming languages, as well as various aspects of natural language processing. Context-free languages are recognized by context-free grammars and can be parsed by algorithms like the pushdown automaton. These languages have a well-defined and structured syntax, making them a powerful tool in computational linguistics and the design of compilers for programming languages. One important property to understand about context-free languages is their closure under certain operations. Closure properties describe what happens when you perform various operations on languages from a particular class. In this context, we are interested in whether the union of two context-free languages (L1 ∪ L2) results in a context-free language.

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