1) Consider the following language over = {a, b, c}:

{aⁱb^jc^k : i = j or i = k or j = k; i, j, k 0}

a) Give a context-free grammar that generates this language

b) Show that your grammar is ambiguous

2) Give a context-free grammar generating the following language over

= {a, b, #}:

{x#y : x, y {a, b}^*; |x| |y|}

3) Give a context-free grammar generating the following language over

= {a, b}:

{w : w is not a palindrome; w ^*}

4) Give a context-free grammar generating the following language over

= {0, 1}:

{0ⁿ1^m : m, n 0 and n < 2m}