Problem 1. If f:XY is a function between two sets and AY is a subset, we define the preimage of A to be f1(A)={xXf(x)A}. Show that: (1) If f:XY and {Bi}iI is a family of subsets of Y, then f1(iIBi)=iIf1(Bi) and f1(iIBi)=iIf1(Bi). (2) If BY, then f1(Y\B)=X\f1(B). (3) If g:YZ is another map and CZ, then (gf)1(C)=f1(g1(C))