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\title{CS 141: Advanced Topics in Algorithms \\ Spring 2006 \\ Assignment Brad and Dave}
\author{}
\date{Due:  Thursday, March 30}
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\item \Points{10} \Name{More about Bases} 
  
  Complete the proof we began in class. Let $B_1, B_2 \in B$ and let
  $I_1, I_2 \in I$ such that $I_1 \subseteq B_1$ and $I_2 \subseteq
  B_2$. Recall that we have chosen $B_2$ so that $|B_2 - (I_2 \cup
  B_1)|$ is minimized. Prove that $B_2-B_1 = I_2-I_1$. \textit{(Hint:
  Show that $B_2 - (I_2 \cup B_1)$ is empty.)}

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