Select the following statements that are true.A NFA with 5 states can be converted to an equivalent DFA with 32 states.The pumping lemma can be used to prove a language is regular.If L is a subset of a regular language R, then I must also be regular.00The pumping lemma can be used to prove a language is not regular.The union of two regular languages is also regular.

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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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Select the following statements that are true.
A NFA with 5 states can be converted to an equivalent DFA with 32 states.
The pumping lemma can be used to prove a language is regular.
If L is a subset of a regular language R, then I must also be regular.
00
The pumping lemma can be used to prove a language is not regular.
The union of two regular languages is also regular.

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Step 1: Introduction

Let's analyze each statement:

A NFA with 5 states can be converted to an equivalent DFA with 32 states.
- True: It is true that a Non-deterministic Finite Automaton (NFA) with 5 states can be converted to an equivalent Deterministic Finite Automaton (DFA) with potentially more states. The number of states in the resulting DFA can grow exponentially with the number of states in the NFA. In the worst case, it can be 2^n where n is the number of states in the NFA. So, while it is possible to convert an NFA with 5 states into a DFA with 32 states, the size of the DFA can vary depending on the specific NFA.

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