(2) (Ø* U b) b*O b*O bb*O b*b Simplify each of the following regular expressions.Example: a ((a U b)(b U a) )* U a ( (a Ub) a)* Ua ((b U a) b)*Simplified regular expression: a ((a U b)(b U a))*

Answered: (2) (Ø* u b) b* Ob о bb* О Бь

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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Question

Simplify each of the following regular expressions.
Example: a ((a U b)(b U a) )* U a ( (a Ub) a)* Ua ((b U a) b)*
Simplified regular expression: a ((a U b)(b U a))*

Expert Solution

Step 1: (Ø* U b) b*:

The correct choice is: b*

Break down the given regular expression:

(Ø* U b) b*

Here, Ø represents the empty set, and Ø* represents the set containing only the empty string ε.

The expression (Ø* U b) represents either the empty string ε or the string "b".

Now, b* represents zero or more occurrences of "b".

Thus, when you combine (Ø* U b) with b*, it can represent:

ε followed by zero or more "b"s - This gives "b*", because ε doesn't add any characters.
"b" followed by zero or more "b"s - This can give a single "b", "bb", "bbb", etc.

Given the options:

a) b*

b) bb*

c) b*b

Let's evaluate them:

a) b*

This option matches the first case of our breakdown (ε followed by zero or more "b"s). It also matches the second case because "b" followed by zero "b"s is still "b", and "b" followed by one "b" is "bb", and so on. So, this option is correct.

b) bb*

This option specifically means one "b" followed by zero or more "b"s. It represents strings like "b", "bb", "bbb", etc. While it represents a subset of the strings represented by (Ø* U b) b*, it doesn't cover all possibilities (it doesn't represent ε followed by zero b's, which is just ε). Therefore, this option is incorrect as a complete representation.

c) b*b

This option means zero or more "b"s followed by one "b". It represents strings like "b", "bb", "bbb", etc. However, it doesn't represent the empty string ε, which is part of the strings represented by (Ø* U b) b*. So, this option is also incorrect as a complete representation.

Thus, the correct choice is:

a) b*

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