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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 ? 

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

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