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What is the differene between {  Φ }  and  λ  and what happens when we concatenate this with a regular language  ??

• any language is concatenation with $\Phi$ is equal to $\Phi$

1)a.$\Phi$ =$\Phi$

2)a*.$\Phi$ =$\Phi$

• any language(x) is concatenation with $\lambda$ is is equal to X. (except  $\lambda$.$\Phi$= .$\Phi$)

1)a. $\lambda$ =a

2)a*. $\lambda$=a*

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Epsilon is concatenation identity and phi is addition identity. Just an extra point