title: Determine whether a grammar is an LL using pairwise disjoint test
body: <p>I have three grammars: </p>
  
  <p>A -> aB | b | CBB</p>
  
  <p>B -> aB | ba | aBb</p>
  
  <p>C -> aaA | b | caB</p>
  
  <p>I need to "determine whether [they] are LL grammars by performing the pairwise disjoint test, showing the first sets of each RHS of each nonterminal.</p>
  
  <p>This is what I have so far...</p>
  
  <p>A -> aB | b | CBB</p>
  
  <p>first(aB) = a</p>
  
  <p>first(b) = b</p>
  
  <p>first(CBB) = aaA = a</p>
  
  <p>This is the one I'm having trouble with. Did I do CBB correctly? If so I would say that they intersect &amp; the rule fails the test. (right?)</p>
  
  <p>B -> aB | ba | aBb</p>
  
  <p>first(aB) = a</p>
  
  <p>first(ba) = b</p>
  
  <p>first(aBb) = a</p>
  
  <p>They are intersected &amp; thus the rule fails the test. </p>
  
  <p>C -> aaA | b | caB</p>
  
  <p>first(aaA) = a</p>
  
  <p>first(b) = b</p>
  
  <p>first(caB) = c</p>
  
  <p>They are not intersected &amp; thus the rule passes</p>