1. (Sets) We will use set theory to define probability spaces. Are these statements true or false? Provide a proof if they are true (you can use Venn diagrams to gain intuition, but also write down a formal proof), or a counterexample if they are false. A partition of a set 2 is a collection of sets S1, ..., Sn such that 0 = U;S; and SinS; = 0 for i # j. (a) If S1, ..., Sn is a partition of 2, then for any subset A C n, SinA, ..., SnnA is a partition of A