Select all true statements1 pointThere are languages A, B such that A is regular, B is undecidable, and A is a superset of B.There are languages A, B such that A is regular, B is undecidable, and A is a subset of B.There are languages A, B such that A is context-free, B is undecidable, and A is a subset of B.There are languages A, B such that A is context-free, B is undecidable, and A is a superset of B.
Question
Select all true statements1 pointThere are languages A, B such that A is regular, B is undecidable, and A is a superset of B.There are languages A, B such that A is regular, B is undecidable, and A is a subset of B.There are languages A, B such that A is context-free, B is undecidable, and A is a subset of B.There are languages A, B such that A is context-free, B is undecidable, and A is a superset of B.
Solution
The correct statement is: "There are languages A, B such that A is regular, B is undecidable, and A is a subset of B."
Here's why:
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"There are languages A, B such that A is regular, B is undecidable, and A is a superset of B." - This is false. A regular language (A) cannot be a superset of an undecidable language (B) because regular languages are a subset of decidable languages.
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"There are languages A, B such that A is regular, B is undecidable, and A is a subset of B." - This is true. A regular language (A) can be a subset of an undecidable language (B). For example, the language of all strings over {0,1} is undecidable, but it includes the regular language of all strings of 0s.
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"There are languages A, B such that A is context-free, B is undecidable, and A is a subset of B." - This is true. A context-free language (A) can be a subset of an undecidable language (B). For example, the language of all strings over {0,1} is undecidable, but it includes the context-free language of all palindromes over {0,1}.
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"There are languages A, B such that A is context-free, B is undecidable, and A is a superset of B." - This is false. A context-free language (A) cannot be a superset of an undecidable language (B) because context-free languages are a subset of decidable languages.
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