2.

a) Use the Context-Free Pumping Lemma (Theorem 8.1) to prove that the language {a^i b^j a^i b^j : i, j } is not context-free.

b) . Use the previous result and closure of context-free languages under intersection with regular sets (Theorem 8.5) to prove that the language {ww : w {a, b}*} is not context-free.