Consider the two languages L₁ = {w₁₂ : |w₁| = |w₂|, w₁∈ {a,b}*, w₂∈ {c,d}* } and L₂ = {a,c}*.

1. L₁∩L₂ is context free but not deterministic context free language.
2. We can draw determinitic pushdown automata with the help of 4 states for language L₁∩L₂.

Which of the following option is correct?
(A) Statement (1) is true and statement (2) is false.
(B) Statement (1) is false and statement (2) is true.
(C) Both statement (1) and (2) are true.
(D) Both statement (1) and (2) are false.


Answer: (B)

Explanation: L₁∩L₂ = {aⁿcⁿ : n ≥ 0} which is deterministic context free language. It\’s (L₁∩L₂) non-deteministic pushdown automat is:

Hence, statement (1) is false and statement (2) is true.

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