If � 1 L 1 is decidable and � 2 L 2 is recognisable then (select all that apply): The following checkbox options contain math elements, so you may need to read them in your screen reader's “reading” or “browse” mode instead of “forms” or “focus” mode. Choice 1 of 3: � 1 ∪ � 2 L 1 ∪L 2 is decidable. Choice 2 of 3: � 1 ∪ � 2 L 1 ∪L 2 is not decidable. Choice 3 of 3:Not enough information to answer.
Question
If � 1 L 1 is decidable and � 2 L 2 is recognisable then (select all that apply):
The following checkbox options contain math elements, so you may need to read them in your screen reader's “reading” or “browse” mode instead of “forms” or “focus” mode. Choice 1 of 3: � 1 ∪ � 2 L 1 ∪L 2 is decidable. Choice 2 of 3: � 1 ∪ � 2 L 1 ∪L 2 is not decidable. Choice 3 of 3:Not enough information to answer.
Solution
Choice 1 of 3: L1 ∪ L2 is decidable.
This is because if a language is decidable, then it remains decidable even when unioned with a recognizable language. The decidable language provides a method for always determining membership, and this method can be used for the unioned language.
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