Testbook Regular expressions

Question

Answer 1

let the symbols be a,b for the language... and L non empty(given)

1)TRUE:

 ∑ * = (a+b) * = { ε , a ,b, ab, ba , aa, ...............................}

let L = { a}  ( to make it more easy)

so ,  ∑ * / L = { ε/a , a/a , b/a , aa/a, ab/a , ba/a,aaa/a ,aba/a..............  }

                 = { ϕ ,ε, ϕ , a, ϕ , b, aa ,ab ...................................}

                 = { ε , a ,b, ab, ba , aa, ...............................} = (a+b)* =  ∑ *

2) FALSE:

L /  ∑ * = { a/ε , a/a ,a/b , a/aa...................................}

           = { a , ε, ϕ , ϕ   ................................} ={ε ,a}

            ≠ ϕ 

3)FALSE :

a*ba*/a* = { a*ba* /ε ,  a*ba*/a ,   ................., a*ba*/a* }

             = { a*ba* ,  a*ba⁺ , a*b }

             = { a*ba*}  ≠ {a*b)

Therefore , only I is true. option c

 

 

Comments

ok thanks:)

---

arvin can you tell me how  $\large \frac{ε}{ε}$ in 1st part

---

brother that was a mistake... it should have been ε/a... thanks for pointing that out :)