MadeEasy Subject Test 2019: Theory Of Computation - Regular Languages

Question

Can anyone explain how S2 is false,I did not understand their logic.

Comments

See here they're talking about equality

if a language  accept epsilon

if we  subtract epsilon from the lang than its not remain the same language anymore than it become totally a different lang right ???

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So L+ isn't a different language,I did not understand this.

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Hey suppose Σ = {a,b} then we know 

Σ* = { epsilon , a, b, aa , ab, ba ,bb ,........}

Here's definition of Language : A language is a set of string all of which are chosen from some ∑*, where ∑ is a particular alphabet.

So a Language can be anything as  well as : L = { epsilon } is also a valid language.( A language that excepts empty

Now L* will obviously be L* = {epsilon} so , L* - {epsilon} = empty set. So second statement will not be always true. I have no formal answer but I hope this counter example I provided helps

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Nice

Thanks :)

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This example helped thanks a lot :p

Answer 1

Because L* will definitely contain Epsilon in it.

Suppose L = {a,b},

then L* = { epsilon , a , b ,aa, ab, ba, bb, ........}

Therefore L* - {epsilon} = {a, b, aa, ab, ba, bb, ..........}

Thus L* - {epsilon} is not equal to L*

Comments

It's L+ not L*

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sorry, the image was not clear. anyway this was my first answer and I don't know if we can delete our answers. Can we delete our answers?