Let  and let Ai ⊂ A and Bi ⊂ B for i = 0 and i = 1. Show that f−1 preserves inclusions, un...

Let  and let Ai ⊂ A and Bi ⊂ B for i = 0 and i = 1. Show that f−1 preserves inclusions, unions, intersections, and differences of sets:

(a) .

(b) .

(c) .

(d) .

Show that f preserves inclusions and unions only:

(e) .

(f) .

(g) .

(h) .