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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?
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- If A ≤m B and B is recursive then A is recursive.
- If A ≤m B and A is undecidable then B is undecidable.
- If A ≤m B and B is recursively enumerable then A is recursively enumerable.
- If A ≤m B and B is not recursively enumerable then A is not recursively enumerable.
- If A ≤m B and B is recursive then A is recursive.
Correct Option: D
If B is not recursively enumerable then A need not be recursively enumerable.