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← Logic & PuzzlesIf a finite state machine transitions according to Kleene's theorem, which outcome concerning the set of recognizable languages results?
A)Becomes non-regular under complement
B)Cardinality increases with each union
C)Remains regular under set operations✓
D)Grows exponentially after intersection
💡 Explanation
Kleene's theorem ensures that regular languages remain regular under union, concatenation, and Kleene star; because the finite state machine operations correspond to these set operations, the recognizable languages remain regular. Therefore, set operations preserve regularity, rather than destroying it, because Kleene's theorem is specifically designed to guarantee this.
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