Question

If a language(L1) is Recursive enumerable  (RE)  and  L2 is Recursive   (REC)  , then  what  will be L1 - L2  ? Can we  directly use set difference property   or do the so called  intersection method  i.e  L1 - L2 = L1 ∩ L2 .

Comments

Always remember that a language is a set of strings, so yes you can apply set difference property. See Arjun Sir's answer: https://gateoverflow.in/2190/gate2010-17?show=2381#a2381

Answer 1

L1 = RE
L2 = REC
L1-L2 = L1 ∩ L2^c = RE ∩ REC = RE ∩ RE = RE

As, REC is closed under complement and RE is closed under intersection.

Comments

A-B = A∩Bc is correct and RE is correct answer

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Ok , So we cannot take  SET DIFFERENCE   DIRECTLY ,  ALWAYS TO USE  L1- L2 = L1 ∩ L2^c. 

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@Sandeep no need to memorize, try to understand the difference why is REC closed under set difference but not RE. REC is closed under set difference because it is closed under INTERSECTION and COMPLEMENT and RE is not closed under set difference because RE is not closed under COMPLEMENT.

Answer 2

https://gateoverflow.in/2190/gate2010-17