title: Is it possible for a subset of a non-context free language to be context-free?
body: <p>For example, if I have a non-context free language of B, is there such a context free language A such that A is a subset of B? I have been thinking of examples but unable to think of any valid ones.
   I thought I got it when I said that <code>A = {A = {w | w is of even length and w ∈ {a, b, c}}</code>, which is context-free, and <code>B = {ww | w ∈ {a,b,c}}</code>, which is not context free. However, I realized that there are some strings A can produce that B cannot, and therefore, A is not a subset of B. </p>
  
  <p>Does anyone know of any examples that could be valid in my situation?</p>