Can someone give me hint how to prove that for a function $f:X\rightarrow Y$ and $B\subseteq X$ we have $f(B)=\emptyset \Rightarrow B=\emptyset \ ?$
Is my idea that, supposing $x\in B\neq \emptyset$, we would have to have, since $f$ is a function, a $y$ such that $f(x)=y$ and therefore $y\in f(B)=\emptyset$, which is a contradiction, correct ?