1. 1a.Write without using P. (Recall P() means power set.)

1b.Suppose S T are nonempty sets. For each of the following four propositions, say whether its guaranteed to be true, guaranteed to be false, or possibly true / possibly false, and justify your answer. S P(T) S P(T) P(S) P(T) P(S) P(T)

1c. Write {a}{b,c}{a,b,c} without using .

1d. Suppose and are two alphabets such that = . Does this imply that = ? Why or why not?

1e. Let f : {2,3,4}{4,5,6} {0,1,2,3} be the function defined by f(x,y) = y mod x. Write the 2-dimensional table representing f.