Let f:X→Y and A,B are non-void subsets of Y, then (where the symbols have their usual interpretation)
A f⁻¹(A)−f⁻¹(B)⊃f⁻¹(A−B) but the opposite does not hold.
B f⁻¹(A)−f⁻¹(B)⊂f⁻¹(A−B) but the opposite does not hold.
C f⁻¹(A−B)=f⁻¹(A)−f⁻¹(B)
D f⁻¹(A−B)=f⁻¹(A)∪f⁻¹(B)