# Collections of Sets, Problem 1(b)

### Solution

Let X={a,b} and Y={c}. Define $$f:X \rightarrow Y$$ by f(x)=c, for all $$x \in X$$. Now choose A={a}, and B={b}. Then $$A \cap B = \emptyset$$. so $$f(A \cap B)=\emptyset$$. However, f(A)=Y=f(B), so $$f(A) \cap f(B) = Y$$.