1. [12 pts] The symmetric difference of sets A and B, denoted by AB, is the set containing those elements in A or B, but not in both A and B. For example, for A={1,2,3} and B={2,3,4,5},AB={1,4,5}. 1. Prove that (AB)B=A. 2. Is the following true: A(BC)=(AB)C ? Prove your answer. 2. [8 pts] Prove that if A and B are two finite sets, then ABAB. Determine when this relationship is an equality. 3. [10 pts] An ordered pair (a,b) differs from a set of two elements {a,b} since the elements of a set are unordered. But we can represent an ordered pair ir terms of sets. Introduce a set-based formulation of ordered pairs and prove that (a,b)=(c,d) under your set-based formulation if and only if a=c and b=d