Show that L1 = L1L2/L2 is not true for all languages L1 and L2
Question
Show that L1 = L1L2/L2 is not true for all languages L1 and L2
Solution
To show that L1 = L1L2/L2 is not true for all languages L1 and L2, we can provide a counterexample.
Let's consider two languages L1 and L2 over the same alphabet.
Let L1 = {a} and L2 = {b}.
L1L2 would then be {ab}, the concatenation of L1 and L2.
The operation L1L2/L2 is defined as the set of all strings w such that for some string x in L2, wx is in L1L2.
In this case, there is no string w such that wx (where x is a string in L2) is in L1L2.
Therefore, L1L2/L2 is the empty set, which is not equal to L1.
So, L1 = L1L2/L2 is not true for these languages L1 and L2.
This counterexample shows that the statement is not true for all languages L1 and L2.
Similar Questions
If L1 is regular L2 is unknown but L1-L2 is regular ,then L2 must be
f L1 and L2′ are regular languages, L1 ∩∩ (L2′ U L1′)’ will be _____.a)all of the mentionedb)may be regularc)regulard)none of the mentionede)non regular
Let L1 = L (a∗baa∗) and L2 = L (aba∗). Find L1/L2
Let L be a regular language on some alphabet Σ, and let Σ1 ⊂ Σ be a smalleralphabet. Consider L1, the subset of L whose elements are made up only ofsymbols from Σ1, that is,L1 = L ∩ Σ∗1 .Show that L1 is also regular.
We can represent one language in more one FSMs, true or false?ans.Cannot be saidTRUEFALSEMay be true
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.