vi. if A is regular, then {xy : x € A, y # A} is regular. vii. If A is regular and B is non-regular, then AB is non-regular. viii. If A is regular and B is non-regular, then AUB is non-regular. ix. If A and B are both non-regular, then An B is non-regular. x. If A is non-regular, then A* is non-regular.

Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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  1. For each of the following statements about regular expressions α, β and languages A, B, state whether they are true or false. Provide a one-sentence justification for each answer.

vi. if A is regular, then {xy : x € A, y & A} is regular.
vii. If A is regular and B is non-regular, then AB is non-regular.
viii. If A is regular and B is non-regular, then AUB is non-regular.
ix. If A and B are both non-regular, then An B is non-regular.
x. If A is non-regular, then A* is non-regular.
Transcribed Image Text:vi. if A is regular, then {xy : x € A, y & A} is regular. vii. If A is regular and B is non-regular, then AB is non-regular. viii. If A is regular and B is non-regular, then AUB is non-regular. ix. If A and B are both non-regular, then An B is non-regular. x. If A is non-regular, then A* is non-regular.
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