3 votes 3 votes Consider the following statements regarding alphabet and language inequalities. Which of the above statements are always true? Answer is S1. Why S2 is False ? It's ME Test Que Aakash_ asked Oct 30, 2018 • edited Oct 30, 2018 by Aakash_ Aakash_ 895 views answer comment Share Follow See all 11 Comments See all 11 11 Comments reply Verma Ashish commented Oct 30, 2018 reply Follow Share statements?? 0 votes 0 votes Aakash_ commented Oct 30, 2018 reply Follow Share Verma Ashish I uploaded the image again, please check 0 votes 0 votes Aakash_ commented Oct 30, 2018 reply Follow Share Star Closure of Language contains empty L0 = {ϵ} so if we remove {ϵ}, it should be L+ .Right ? 0 votes 0 votes Mk Utkarsh commented Oct 30, 2018 reply Follow Share Aakash_ yes right What explanation they gave for $S_2$ 0 votes 0 votes Verma Ashish commented Oct 30, 2018 reply Follow Share Yes ,,but there may be something which we are missing.. I'm thinking... 0 votes 0 votes Aakash_ commented Oct 30, 2018 reply Follow Share Explanation, and i am not able to understand this, why RHS will contain empty string ? 1 votes 1 votes Verma Ashish commented Oct 30, 2018 reply Follow Share L+ = L•L* Can we verify explanation by taking L={ϵ} ?? 0 votes 0 votes Swapnil Naik commented Oct 30, 2018 i edited by Swapnil Naik Oct 30, 2018 reply Follow Share If L={$\epsilon$} then L* = {$\epsilon$} L.H.S = L*- {$\epsilon$} = L* $\cap$ $\sum$+ = $\epsilon$ $\cap$ $\sum$+ = $\phi$ R.H.S. = L+=LL* = $\epsilon$.$\epsilon$ = $\epsilon$ L.H.S $\neq$ R.H.S 8 votes 8 votes Aakash_ commented Oct 30, 2018 reply Follow Share Swapnil Naik Thanks for your Answer. 1 votes 1 votes Deepalitrapti commented Jun 15, 2019 reply Follow Share Swapnil naik we can take same example for statement s1 ?? 0 votes 0 votes Swapnil Naik commented Jun 15, 2019 reply Follow Share @Deepalitrapti $\sum$ is set of symbols, where as $\epsilon$ is an empty string. So we can have $\sum$ = {a, b} where a and b are character/symbols, but for $\epsilon$ its a string and hence can not be a part of an alphabet. https://math.stackexchange.com/questions/1689850/is-the-empty-string-always-in-a-finite-alphabet 0 votes 0 votes Please log in or register to add a comment.