# prove that language is not a language without context

Prove that language $${a ^ i b ^ jc ^ k$$ $$|$$ $$i> j> k geq 0 }$$ is a context free language without using the pumping lemma.

we could use some useful facts to solve the question:

1. $$A$$ is a language without context and $$B$$ is regular, then $$A cap B$$ is without context.
2. $$L_1$$, $$L_2$$ are not languages ​​without context, the intersection $$L_1 cap L_2$$ nor is it devoid of context.