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Select all true statements. A and B are some decidable language. The statements should be true irrespective of what A and B are.1 pointA ≤ BB ≤ AA ≤ HALTSHALTS ≤ BA ≤ A

Question

Select all true statements. A and B are some decidable language. The statements should be true irrespective of what A and B are.1 pointA ≤ BB ≤ AA ≤ HALTSHALTS ≤ BA ≤ A

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Solution

The statements that are always true irrespective of what A and B are:

  1. A ≤ B: This statement is true because every language is reducible to itself and to any other language that contains it.

  2. B ≤ A: This statement is also true because every language is reducible to itself and to any other language that contains it.

  3. A ≤ A: This statement is true because every language is reducible to itself.

The statements that are not necessarily true:

  1. A ≤ HALTS: This statement is not necessarily true. The halting problem (HALTS) is undecidable, and not all decidable languages can be reduced to it.

  2. HALTS ≤ B: This statement is also not necessarily true. The halting problem (HALTS) is undecidable, and it cannot be reduced to a decidable language.

So, the true statements are A ≤ B, B ≤ A, and A ≤ A.

This problem has been solved

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