Proof Note that \(\emptyset^c = S\text{.}\) So, by the theorem above 4.3.4, \begin{equation*} 1 = P(S) + P(\emptyset) \Rightarrow 1 = 1 + P(\emptyset). \end{equation*} Cancelling the 1 on both sides gives \(P(\emptyset) = 0\text{.}\)