Answer
{ }, {dog}, {cat}, {fish}, {dog,cat}, {dog,fish}, {cat,fish}, {dog,cat,fish}
Work Step by Step
List all the subsets with 0 members { }
List all the subsets with 1 member {dog}, {cat}, {fish}
List all the subsets with 2 members {dog,cat}, {dog,fish}, {cat,fish}
List all the subsets with 3 members {dog,cat,fish}