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