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Consider the following language $L$ over the alphabet $\Sigma=\{a, b, c\}$. $$ L=\left\{a^{i} b^{j} c^{k} \mid i, j, k \geq 0 \text {, and if } i=1 \text { then } j=k\right\} $$

  1. Show that $L$ is not regular.
  2. Show that $L$ is a context-free language.
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