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

Question

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

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Solution

The given conditions are A ≤ B, B ≤ C, and C is undecidable. Here, the symbol "≤" represents "is reducible to".

  1. A is decidable: This could be true or false. It depends on what A is. If A is a problem that can be reduced to B and B can be reduced to C, it doesn't necessarily mean that A is undecidable just because C is. A could still be a decidable problem.

  2. A is undecidable: This could also be true or false. It depends on what A is. If A is a problem that can be reduced to an undecidable problem, it could potentially be undecidable, but it's not guaranteed.

  3. B is decidable: This is likely false. Since B can be reduced to C and C is undecidable, it's likely that B is also undecidable. However, it could depend on the specifics of what B is.

  4. B is undecidable: This is likely true. Since B can be reduced to C and C is undecidable, it's likely that B is also undecidable. However, it could depend on the specifics of what B is.

  5. A could be decidable or undecidable, it depends on what A, B, C are: This is true. As explained above, A could be either decidable or undecidable depending on its specifics.

  6. B could be decidable or undecidable, it depends on what A, B, C are: This is likely false. Given the conditions, it's likely that B is undecidable. However, there could be specific cases where this is not true.

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