If A = {abc, def, g} and B = {1, 2), the concatenation of A and B is {abc1, def1, g1, abc2, def2, g2). In other words, the concatenation of two languages A and B is the set of all strings vw, where v is a string in A, and w is a string in B. %3D %3! Now consider the following languages: N = {the dog, the cat, the mouse} and V = {runs} Check all true statements about N, V and their concatenation. Both N and V are regular languages, and the concatenation of N and V is a regular language. Both N and Vare regular languages, but the concatenation of N and V is not a regular language. The string "the cat runs" is in the language defined by the concatenation of N and V. The string "the dog the cat" is in the language defined by the concatenation of N and V. D The string "runs the dog" is in the language defined by the concatenation of N and V. 010 If L is a formal language that contains finitely many strings, the language L,* , which contains infinitely many strings, is a regular language. O True O False
If A = {abc, def, g} and B = {1, 2), the concatenation of A and B is {abc1, def1, g1, abc2, def2, g2). In other words, the concatenation of two languages A and B is the set of all strings vw, where v is a string in A, and w is a string in B. %3D %3! Now consider the following languages: N = {the dog, the cat, the mouse} and V = {runs} Check all true statements about N, V and their concatenation. Both N and V are regular languages, and the concatenation of N and V is a regular language. Both N and Vare regular languages, but the concatenation of N and V is not a regular language. The string "the cat runs" is in the language defined by the concatenation of N and V. The string "the dog the cat" is in the language defined by the concatenation of N and V. D The string "runs the dog" is in the language defined by the concatenation of N and V. 010 If L is a formal language that contains finitely many strings, the language L,* , which contains infinitely many strings, is a regular language. O True O False
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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Question
Transcribed Image Text:If A = {abc, def, g} and B = {1, 2), the concatenation of A and B is {abc1, def1, g1, abc2, def2, g2). In
other words, the concatenation of two languages A and B is the set of all strings vw, where v is a
string in A, and w is a string in B.
%3D
%3!
Now consider the following languages:
N = {the dog, the cat, the mouse}
and
V = {runs}
Check all true statements about N, V and their concatenation.
Both N and V are regular languages, and the concatenation of N and V is a regular language.
Both N and Vare regular languages, but the concatenation of N and V is not a regular language.
The string "the cat runs" is in the language defined by the concatenation of N and V.
The string "the dog the cat" is in the language defined by the concatenation of N and V.
D The string "runs the dog" is in the language defined by the concatenation of N and V.
010
Transcribed Image Text:If L is a formal language that contains finitely many strings, the language L,* , which contains
infinitely many strings, is a regular language.
O True
O False
Expert Solution
Step 1
Concatenation of Language P and Q
The set of strings that may be generated by combining any string from P and concatenating it with string of any kind from Q is known as the concatenation of languages P and Q, abbreviated P.Q or simply PQ.
Example
If P= {011, 10, 111} and Q = {epsilon, 001} then
P.Q = {011, 10, 111, 011001, 10001, 111001}
Given N = {the dog, the cat, the mouse}
V = {runs}
The concatenation of N and V is : N.V = {the dog runs, the cat runs, the mouse runs}
V.N = {runs, runs the dog, runs the cat, runs the mouse}
If P and Q are regular expressions, then EF will be a regular expression referring the L(P) and L(Q ) concatenation. That is, L(PQ) = L(P).L(Q )
Therefore option 1 is true and option 2 is false
The concatenation of N and V is {the dog runs, the cat runs, the mouse runs}
Therefore option 3 is correct whereas option 3 and option 4 is not correct.
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