(1) If L₁ and L2 are context free, then it is possible that L₁ L₂ is not context free. True O False

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
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**Question:**

(1) If \( L_1 \) and \( L_2 \) are context free, then it is possible that \( L_1 \cap L_2 \) is not context free.

- ○ True
- ○ False

**Explanation:**

This question addresses the properties of context-free languages. While the union of two context-free languages is always context-free, their intersection is not necessarily context-free. This property distinguishes context-free languages from regular languages, where both union and intersection are closed operations. The answer is "True."
Transcribed Image Text:**Question:** (1) If \( L_1 \) and \( L_2 \) are context free, then it is possible that \( L_1 \cap L_2 \) is not context free. - ○ True - ○ False **Explanation:** This question addresses the properties of context-free languages. While the union of two context-free languages is always context-free, their intersection is not necessarily context-free. This property distinguishes context-free languages from regular languages, where both union and intersection are closed operations. The answer is "True."
Expert Solution
Step 1: Introduce context free grammar

In the realm of formal languages, the closure properties of language  classes dictate what operations can be performed on languages within those classes while maintaining membership in the same class. One  important class of languages is the context-free languages. In the next step, we will explore the closure property related to the intersection of two context-free languages shedding light on why the intersection of context-free languages may not always yield a context-free language.

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