   Chapter 12.1, Problem 4ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# In 4—6, describe L 1 L 2 ,   L 1 ∪ L 2 , and ( L 1 ∪ L 2 ) * for the given languages L 1 and L 2 .4. L 1 iis the set of all strings of a’s and b’s that start with an a and contain only that one a ;   L 2 is the set of all strings of a’s and b’s that contain an even number of a’s.

To determine

Find L1,L2,L1L2and(L1L2)* for the given languages L1andL2.

Explanation

Given information:

Describe L1,L2,L1L2and(L1L2)* for the given languages L1andL2.

Concept used:

“ Set of all strings of a's and b's that start with an a and contain an odd number of a's

“ Set of all strings of a's and b's that contain an even number of a's or that starts with an a

and contain only that one a

“ Set of all strings of a's and b's

Calculation:

It is given that L1 is the set of all strings of a's and b's that start with an a and contain only that

one a and L2 is the set of all strings of a's and b's that contain even number of a's.

L1L2 represents concatenation of the language L1 and L2 so, L1L2 has odd number of a's that

is one a from L1 and even number of a's from L2 so, it can be described as:

“ Set of all strings of a's and b's that start with an a and contain an odd number of a's

L1L2 is described as:

“ Set of all strings of a's

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