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: 4

Answer

$L1 $is the set of all strings of a’s and b’s that begins with an a and contain only that one a; $ L2$ is the set of all strings of a’s and b’s that contain an even number of a’s.

Work Step by Step

$L1 $is the set of all strings of a’s and b’s that start with an a and contain only that one a; $ L2$ is the set of all strings of a’s and b’s that contain an even number of a’s. --$L_1L_2$ is the set of all strings of a’s and b’s that begins with an a and contain an odd number of $a’s$. $L1∪L2$ is the set of all strings of a’s and b’s that contain an even number of a’s or that start with an a and contain only that one a. ($L1 ∪ L2$) ∗ is the set of all strings of a’s and b’s. The reason is that a and b are both in $L1 ∪ L2$, and thus every string in a and b is in $(L1 ∪ L2) *$.
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