(5) If L is context free, then L¬L must also be 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:**

(5) If \( L \) is context free, then \( L \cap \lnot L \) must also be context free.

- [ ] True
- [ ] False

**Explanation:**

This question tests the understanding of closure properties of context-free languages. Context-free languages are not closed under the complementation operation. Therefore, \( \lnot L \) may not be context-free, and the intersection of a context-free language \( L \) with a non-context-free language \(\lnot L\) is not guaranteed to be context-free. Consider carefully whether the statement is true or false based on these closure properties.
Transcribed Image Text:**Question:** (5) If \( L \) is context free, then \( L \cap \lnot L \) must also be context free. - [ ] True - [ ] False **Explanation:** This question tests the understanding of closure properties of context-free languages. Context-free languages are not closed under the complementation operation. Therefore, \( \lnot L \) may not be context-free, and the intersection of a context-free language \( L \) with a non-context-free language \(\lnot L\) is not guaranteed to be context-free. Consider carefully whether the statement is true or false based on these closure properties.
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