Ullman (TOC) Edition 3 Exercise 7.2 Question 5 (Page No. 287)

Question

Use Ogden's lemma $($Question $3)$ to show that the following languages are not $CFL's:$

1. $\{0^{i}1^{j}0^{k}|k=max(i,k)\}.$
2. $\{a^{n}b^{n}c^{i}|i\neq n\}.$ Hint$:$ If $n$ is the constant for Ogden's lemma,consider the stirng $z=a^{n}b^{n}c^{n+n!}.$