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Suppose A ≤ B and B is undecidable, then:1 pointA is decidableA is undecidableA could be decidable or undecidable. It depends on what A and B are.

Question

Suppose A ≤ B and B is undecidable, then:

1 point

  • A is decidable
  • A is undecidable
  • A could be decidable or undecidable. It depends on what A and B are.
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Solution

The correct answer is: A could be decidable or undecidable. It depends on what A and B are.

Here's why:

The statement "A ≤ B" means that A is reducible to B. In other words, if we can solve B, we can solve A. However, we know that B is undecidable, meaning there is no algorithm that can determine the answer for all inputs.

Now, if A is decidable, then there exists an algorithm that can solve A for all inputs. This doesn't contradict our earlier statement, because it's possible that A is a simpler problem than B.

On the other hand, if A is undecidable, then there is no algorithm that can solve A for all inputs. This also doesn't contradict our earlier statement, because it's possible that A is just as complex as B, or even more complex.

So without knowing more about what A and B are, we can't definitively say whether A is decidable or undecidable. It could be either.

This problem has been solved

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