1. . Let A = {1,2,3,4,5}, B = {1,3,5,7,9}, and C ={2,6,10,14}.
a. Compute the following sets: A?B, A?B, B?C, B?C, AB, BA.
b. Compute the following sets: A?(B?C), (A?B)?(A?C), A?(B?C),(A?B)?(A?C).
c. Prove that A?B = (AB)?(A?B)?(BA).
2. Let C0 = {3n : n ? Z} = {...,?9,?6,?3,0,3,6,9,...} C1 = {3n+1: n ? Z} = {...,?8,?5,?2,1,4,7,10,...} C2 = {3n+2 : n ? Z} ={...,?7,?4,?1,2,5,8,11,...}.
a. Prove that the sets C0, C1, and C2 are pairwise disjoint.
b. Compute C0 ?C1 ?C2.
3. Let R>0 be the set of positive real numbers, that is,R>0 = {x ? R : x > 0}.
Prove that {e x : x ? R} = R>0 and {logx : x ? R>0} =R.
