2.9-2.11, due on January 16

I found the Example 2.24 in section 2.10 to be difficult to understand upon first reading. 

"Suppose that we are considering the set A = {1 , 2, 3} and its power set P( A), the set of all subsets of A. Then the quantified statement for every set B ∈ P( A), A− B = ∅. (2.6) is false since for the subset B = A = {1 , 2, 3} , we have A− B = ∅."

I guess I am still struggling with the principles of sets, subsets, power sets, and empty sets.  I had to reread many times the following, B ∈ P( A), A− B = ∅ is false, before I grasped what it was trying to say about the relationship between B and the power set P( A).  I understand now, but it was difficult for a little while.

The most interesting part to me was the discussion of how mathematicians rarely use the definition in an "if and only if" statement.  To me it seemed a valid characterization of an equilateral triangle.  "A triangle T is equilateral if and only if T has three equal sides."  However, I learned that this is not a characterization, but rather a definition.  An accurate characterization of equilateral triangles was presented, "A triangle T is equilateral if and only if T has three equal angles."  I quickly understood the difference and found it to be an interesting point as I look forward to other examples of this in future chapters.