Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 12 - Regular Expressions and Finite-State Automata - Exercise Set 12.1 - Page 790: 13

Answer

{e, ab}

Work Step by Step

using set notation to derive the language defined by the e | ab regular expression. Assuming $\Sigma$ = {a, b, c}. $L(e | ab) = L(e) ∪ L(ab) = {e} ∪ L(a)L(b)$ $= ({e}) ∪ {xy | x ∈ L(a) and y ∈ L(b)}$ $= ({e}) ∪ {xy | x ∈ {a} and y ∈ {b}}$ $= ({e}) ∪ {ab} = {e, ab}$
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