Explanation Given: A and B are regular sets. By Kleene’s theorem,a set is regular if and only if it is recognized by a finite-state automaton. Since, A is regular, so there isa finite-state automaton M that accepts A. By just changing the final states to the non-final states and the non-final states to final states of this machine we obtain a machine that accepts A ¯ . Thus, by Kleen’s theorem, A ¯ is regular. Similarly B ¯ is also regular. Now, by the definition of regular sets, if two sets are regular then their union is also regular. Thus, A ¯ ∪ B ¯ is also regular

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ISBN: 9781266712326

Author: ROSEN

Publisher: MCG CUSTOM

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

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Chapter 13, Problem 24SE

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If A and Bare regular sets then, A∩B is also regular.

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Chapter 13, Problem 23SE

Chapter 13, Problem 25SE

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To show that: If A and Bare regular sets then, A ∩ B is also regular.

Solution Summary: The author explains Kleene's theorem that a set is regular if it is recognized by finite-state automatons. If two sets are regular, their union is also regular.

Concept explainers

To show that:

If A and Bare regular sets then, A∩B is also regular.

Want to see the full answer?

Chapter 13 Solutions

To show that: If A and Bare regular sets then, A ∩ B is also regular.

Solution Summary: The author explains Kleene's theorem that a set is regular if it is recognized by finite-state automatons. If two sets are regular, their union is also regular.

Concept explainers

To show that: If A and Bare regular sets then, A∩B is also regular.

Want to see the full answer?

Chapter 13 Solutions

To show that:

If A and Bare regular sets then, A∩B is also regular.