ISRO2017-77

Question

If $L$ and $P$ are two recursively enumerable languages then they are not closed under

• A. Kleene star $L^*$ of $L$
• B. Intersection $L \cap P$
• C. Union $L \cup P$
• D. Set difference

Comments

what is wrong in this question?

Answer 1

Set difference=$L-P =L\cap P^{C}$. Since, recursively enumerable languages are closed under intersection but not under complement, Set difference of these two language is not closed.

Refer : This also 

Comments

Intersection of Recursive and Recursively enumerable language is recursively enumerable (https://gateoverflow.in/237873/recursive-and-recursively-enumerable). If L and P are recursively enumerable then L−P=L∩P' (complement). P' must be recursive. Thus L−P=L∩P' is recursively enumerable (). Thus recursively enumerable is closed under set difference. But you are saying L-P is not closed. Please clarify. 

Answer 2

D) SET DIFFERNCE

Comments

recursively enumerabke languages are closed under union i tersection and closure..the operation L-P i.e difference can be written as L and ~P since recursively enumerable languages are not closed under complement.so option d is correct