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


Answer: (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

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