Let U be a well defined universe; S be a well defined sample space. Let E= empty set.
Prove or disprove that Pr(E)=0
In the axioms of probability there are at most three axioms.
If $\displaystyle S$ is the space then $\displaystyle P(S)=1$.
If $\displaystyle A\cap B=\emptyset$ then $\displaystyle P(A\cup B)=P(A)+P(B)$.
Using those two it is easy to show that $\displaystyle P(\emptyset)=0 $
Probability axioms - Wikipedia, the free encyclopedia : the second one.