Consider the languages \(L_{1}= \phi\) and \(šæ_2={1}\). Which one of theā¦
2017
Consider the languagesĀ \(L_{1}= \phi\) andĀ \(šæ_2={1}\).Ā Which one of the followingĀ represents \(L_{1}^{\ast}\cup L_{2}^{\ast} L_{1}^{\ast}\)?
- A.
\(\{ā\}\) - B.
\(\{ā,1\}\) - C.
\(š\) - D.
\(1^ā\)
Attempted by 194 students.
Show answer & explanation
Correct answer: D
Key facts: compute each component and simplify.
L1 = ā , so L1* = {Īµ} (only the empty string from zero concatenations).
L2 = {1}, so L2* is the set of all strings of zero or more 1's, i.e. {1}* (this set already contains Īµ).
Concatenate: L2* L1* = {1}* {Īµ} = {1}* (concatenating with {Īµ} leaves the set unchanged).
Union: L1* āŖ (L2* L1*) = {Īµ} āŖ {1}* = {1}* (since Īµ is already in {1}*).
Answer: {1}* ā the set of all strings consisting of zero or more 1's (including the empty string).
A video solution is available for this question ā log in and enroll to watch it.