Which of the following statements is true ?

This question was previously asked in
UGC NET Computer Science (Paper 2) 2020 Official Paper
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  1. The union of two context free languages is context free.
  2. The intersection of two context free languages is context free.
  3. The complement of a context free language is context free.
  4. If a language is context free, it can always be accepted by a deterministic pushdown automaton.

Answer (Detailed Solution Below)

Option 1 : The union of two context free languages is context free.
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UGC NET Paper 1: Held on 21st August 2024 Shift 1
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Detailed Solution

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The correct answer is option1

Key Points

  • Context-free language is closed under Union, Concatenation, and Kleen closure. But not closed under complementation and intersection.
  • If a Language is Context Free, it can be either deterministic or non-deterministic language. only deterministic languages are accepted by the deterministic pushdown automaton.
  • Let L1 and L2 be Context-free language

Option 1: 

L1 ∪ L2 is context-free

As context-free languages are closed under union. So it is correct

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