1. Show that the following languages are not context-free:

a) {a n b mc k | n > m > k}

b) {w {a, b, c} | na(w) > nb(w) > nc(w)}

c) {www | w {a, b} }

d) {a n b mc k | n, m N and k = m n}

e) {a n b m | m = n 2 }

2. Show that the languages {a n | n is a prime number} and {a n 2 | n N} are not context-free. (In fact, it can be shown that a language over the alphabet {a} is context-free if and only if it is regular.)