title: Proving language is context-free with pumping lemma
body: <p>I've got a test coming up in using the pumping lemma to prove whether or not a language is context free. I'm trying to work through some practice problems and things aren't going so great...</p>
  
  <p>The practice problem is:
  For a) through j), prove whether or not the following language is context free or not. If it is context-free, give a context-free grammar that generates it.</p>
  
  <p>The first two are:</p>
  
  <pre><code>a) {a^(2i+1) b^(3k+2) c^(4k+3) d^(5i+4) | i &gt;= 0, k &gt;= 0}
  
  b) {a^i b^i c^k d^i | i &gt;= 1, k &gt;= 1}
  </code></pre>
  
  <p>If someone can solve these first two, giving a detailed explanation of how they did it, I'm sure I'll be able to figure out the rest (c through j) on my own.</p>