inverse function

Question

Q. Let f be a function from A to B. Let S and T be subsets
of B. Show that
a) f⁻¹(S ∪ T ) = f⁻¹(S) ∪ f⁻¹(T ).
b) f⁻¹(S ∩ T ) = f⁻¹(S) ∩ f⁻¹(T ).

Comments

I think first of all we need to check s or t contain any element which are not in range of function f

Like f :A->B, A={1,2,3) B={j,c,d,g,h,k} S={j,d,h} T={d,h,g,k}

f(1)=j

F(2)=d

F(3)=g 

Then -

S∩T={d,h}  S∪T={j,d,h,g,k}

Is F^-1(S∩T) or F^-1(S∪T) possible??