title: Prove big O of addition and subtraction of functions
body: <p>Suppose <code>f(n) = O(s(n))</code> and <code>g(n) = O(r(n))</code>. Prove or disprove (by giving a counter example) the following claims:</p>
  
  <ol>
  <li>f(n) - g(n) = O(s(n) - r(n))  </li>
  <li>if f(n) = O(g(n)), then f(n) + g(n) = O(s(n))</li>
  </ol>
  
  <p>I really have no idea where to even start.. please lend a hand to a young student. Please, give explanations and not just solutions. Thank you so much.</p>