Proof:
We have
[math]\begin{align*}
\href{/cs2800/wiki/index.php/Pr}{Pr}(E)
&= \href{/cs2800/wiki/index.php/Pr}{Pr}(\href{/cs2800/wiki/index.php/S}{S} \href{/cs2800/wiki/index.php/%E2%88%96}{∖} (\href{/cs2800/wiki/index.php/S}{S} \href{/cs2800/wiki/index.php/%E2%88%96}{∖} E)) && \href{/cs2800/wiki/index.php?title=Claim:If_A_%E2%8A%86_B_then_A_%3D_B_%E2%88%96_(B_%E2%88%96_A)&action=edit&redlink=1}{\text{since E = S ∖ (S ∖ E)}} \\
&= 1 - \href{/cs2800/wiki/index.php/Pr}{Pr}(\href{/cs2800/wiki/index.php/S}{S} \href{/cs2800/wiki/index.php/%E2%88%96}{∖} E) && \href{/cs2800/wiki/index.php/Claim:Pr(S_%E2%88%96_E)_%3D_1_-_Pr(E)}{\text{using the fact that Pr(S ∖ E) = 1 - Pr(E) with S ∖ E plugged in for E}} \\
&≤ 1 - 0 = 1 && \href{/cs2800/wiki/index.php/Kolmogorov_axiom}{\text{Since Pr(S ∖ E) ≥ 0}}
\end{align*}
[/math]
