# GATE | GATE-CS-2014-(Set-2) | Question 26

Let A ≤m B denotes that language A is mapping reducible (also known as many-to-one reducible) to language B. Which one of the following is FALSE?

a)  If A ≤m B and B is recursive then A is recursive.
b) If A ≤m B and A is undecidable then B is undecidable.
c) If A ≤m B and B is recursively enumerable then A is recursively enumerable.
d) If A ≤m B  and B is not recursively enumerable then A is not recursively enumerable.
(A) a
(B) b
(C) c
(D) d

Explanation:

• A ≤m B means language A is mapping reducible to language B.Thus, A cannot be harder than B.
Since, A can be reduced to B, instead of deciding A we can now decide B.
So, the first three options are correct.
• As B is not recursively enumerable, it doesn’t guarantee A is not recursively enumerable.Thus, if A ≤m B and B is not recursively enumerable then A is not recursively enumerable. Therefore, answer is D is correct

Please comment below if you find anything wrong in the above post.

Quiz of this Question

My Personal Notes arrow_drop_up
Article Tags :

1

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.