Context-freeness of $\{a^nb^mc^k \mid n \leq m \leq k\}$ and its complement
The language $L_1$ is not context-free, and you can show this using the pumping lemma. Try to pump the word $a^nb^nc^n$ where $n$ is large enough.

The language $L_2$, in turn, is context-free. This is because we can write it as a union of context-free languages:


Words not of the form $a^*b^*c^*$.
Words of the form $a^nb^mc^k$ where $n&gt;m$.
Words of the form $a^nb^mc^k$ where $m&gt;k$.