1. Use the pumping lemma to show that {aⁱ b ^j c^k| i < k and j > k} is not a context-free language.

2. Use the pumping lemma for regular sets to show that {ww^R | w (a + b ) *} is not a regular set.

3. Let L = { aⁿ bⁿ cⁿ dⁿ |n 1 }. Show that L can be expressed as the intersection of two context-free languages.