Is L a context free langauge? context-free grammar? Is $L = \{ a^{(i)} b^{(i)} c^{(j)} \mid i \le j\}$ a context-free language? 
Would i just create a context free grammar for this?

HINT: Try using the Bar-Hillel pumping lemma to show that $L$ is not context-free. If $p$ is the pumping length, start with the word $w=a^pb^pc^p$. The pumping lemma tells you that $w$ can be decomposed as $w=uvxyz$ in such a way that $|vxy|\le p$, $|vy|\ge 1$, and $uv^kxy^kz\in L$ for all $k\ge 0$. Note that since $|vxy|\le p$, at most two of the letters $a,b$, and $c$ can occur in the substring $vxy$. With a bit of thought you can show that no matter where in $w$ the substring $vxy$ appears, you’ll get a word not in $L$ either by pumping up to a $k>1$ or by pumping down to $k=0$.
