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 \(f(A) \cap f(B) = Y\).