# Peter Linz Edition 5 Exercise 11.1 Question 10 (Page No. 284)

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Is the family of recursive languages closed under concatenation$?$

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### Recursive language is closed under concatenation .

Concatenation: If L1 and If L2 are two recursive languages, their concatenation L1.L2 will also be recursive. For Example:

L1= {a^nb^nc^n|n>=0}

L2= {d^me^mf^m|m>=0}

L3= L1.L2

= {a^nb^nc^nd^m e^mf^m|m>=0 and n>=0}

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Let $L_1$ be recursive and $L_2$ recursively enumerable. Show that $L_2-L_1$ is necessarily recursively enumerable.