Finite Automata

Question

Answer 1

We know that, if a language is finite then it is a regular language, but if it is infinite then it can be regualar or may not be regular.

For example: L = { W |  W ending with b and W = { a,b }* }

 L = { b, abbb,aaaabb,. . . . } it is an infiinte language but it is regualar language defined as (a+b)*b.

For second Statement,

let L be language.

L* always contains  ∈, so (L*)' does not contain the  ∈.

But (L')* will contain  ∈, as regular expression with * always contains empty string  ∈.

but (L*)' does not contain  ∈. Hence (L')* ≠ (L*)'.

Hope it helps

Hence S1 is False, Hence D is correct Ans.

Comments

what about S2 sentence ?

---

let L be language.

L* always contains  ∈, so (L*)' does not contain the  ∈.

But (L')* will contain  ∈, as regular expression with * always contains empty string  ∈.

but (L*)' does not contain  ∈. Hence (L')* ≠ (L*)'.

Hope it helps.

Answer 2

d is correct..

Answer 3

D OPTTION AS

TAKE an example of L={a^nb^n | n>=0}

s1 = false, not true for every condition.

s2= from the above example epsilon differ in both so it is true.