1. Is the formula $(x+5)^2 = x^2 + 25$ always true? If it is, find a way to prove that it is true. If it is not, provide a counterexample (a value of $x$ which shows that the formula is not always true).
  2. Write down all the subsets of the following sets:
    1. $\{a,b,c\}$
    2. $\{a,b,c,d\}$
  3. Write down something you notice about the lists of subsets in 2.