NIELIT 2017 DEC Scientist B - Section B: 19

Question

Recursive enumerable languages are not closed under _________.

• A. Set difference
• B. Complement
• C. Both (A) and (B)
• D. None of the options

Answer 1

BOTH A and B

https://courses.engr.illinois.edu/cs373/sp2013/Lectures/lec26.pdf

Answer 2

REL is not closed under complement.
A-B = $A\cap( \sim B)$
As Complement is not closed.
Set difference is also not closed.
Option C.

Comments

But intersection of Recursively enumerable and Recursive language is recursively enumerable. Then

A∩(∼B) must be recursively enumerable.

Answer 3

The answer is C as Recursively Enumerable are closed under every other operation except Set difference and Complementation

Reference: Recursively Enumerable languages

Answer 4

Except Set difference and Complementation,Recursive enumerable language satisfies all the remaining closure properties.

Answer:opt c