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Which of the following statements is true?

  1. If a language is context free it can always be accepted by a deterministic push-down automaton
  2. The union of two context free languages is context free
  3. The intersection of two context free languages is a context free
  4. The complement of a context free language is a context free
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Answer is (B).

(A) is wrong as a language can be context free even if it is being accepted by non-deterministic PDA for ex- $\{ ww^r: w \in \Sigma^*$ and $w^r$  is reverse of $w\}$

(C) and (D) not always true as Context free languages are not closed under Complement or Intersection.

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