#Empty_Language #ϕ #TOC #Doubt #Concatenation

Question

I have a naive doubt about the below statement

L. ϕ = ϕ. L = ϕ

I want to know if the above statement holds true. If yes, can you please explain ? 

Comments

@raja11sep Sir, I have gone through those links already.

I had commented their but the moderator deleted my comment because questions can’t be asked in the answer section/ comment he said !

But my question is “ Is the above diagram correct “ ? If wrong why?

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Transitions while concatenating 2 dfas are supposed to happen from final states to start states.
In case one,  your diagram is correct, and as the dead DFA has no accepting state, the language accepted is eventually NULL.

However, in your second case, there shouldn't be any transition possible at all, because there are no final states to transit from to the start of L.

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@palashbehra5 Thank you I didn’t know about this one :)

Transitions while concatenating 2 dfas are supposed to happen from final states to start states.

Answer 1

∅ in concatenation is similar to 0 in multiplication. x.0 = 0 doesn’t mean x is 0. Similarly L . ∅ = ∅ doesn’t mean L = ∅.

Comments

This is not a proof.