Let A, B and C be three non-empty subsets of a set X and f be a function from X to a set Y (i.e.,f:X→Y).Given some arbitrary D⊆X,by f(D) we denote the set {y ∈ Y |y = f (x) for some x ∈ D}. Prove the following: (a) If A ∩ B ̸= ∅, then f(A ∩ B) ⊆ f(A) ∩ f(B);

(b) f(A ∪ B) = f(A) ∪ f(B).

Been having real problems with this problem. I have just started to study martix algebra so go easy if this might be simple.