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.
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.
Similar Questions
A is some decidable language. Select all statements that are true irrespective of what A is.1 pointHALTS ≤ HALTS'HALTS' ≤ HALTSA ≤ HALTS'HALTS' ≤ A
Which of the following is NOT a property of integer numbers? For two integers 'a' and 'b'.*1 pointa*ba/ba - ba+b
The following are elements of a mathematical system EXCEPT?*1 pointDefined termsEquationsPostulatesUndefined terms
If A = 555! And B = (278)555 then which one of the following relation is appropriate?Cannot be determinedA>BA<BA=B
Which of the following statements is true? A. Point, line, and plane are undefined terms. B. A theorem is an accepted statement of fact. C. "Vertical angles are congruent" is a definition. D. A postulate is a conjecture that is proven.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.