In standard probability theory events are represented by sets consisting of elementary events. Consider two events for which (as sets) $A \subset B$. If an elementary event $x \in A$ takes places then we say that $B$ takes place as well. Since $A \subset B$, $x \in A$ implies that $B$ takes place too.
It seems that when for sets (representing events) $$A \subset B$$ $$then \ A \ implies \ B .$$
On the other hand, if we use the language of logic for the events then $$A \supset B$$ $$ \ means\ that \ A\ implies\ B .$$
Why is this strange virtual contradiction between the language of sets and the language of logic?
(In order to avoid down votes and unplesant comments I reveal that I happen to know that the true translation of the sentence $A \supset B$ of logic to the language of sets (representing events) is $\overline{A \cap \overline B}$.)
Yes, it is inconsistent and confusing.
In logic's defense, the $\supset$ notation for logical implication is rare nowadays; it is more often notated $\to$ (Hilbert, 1922) or $\Rightarrow$ (Bourbaki, 1954) -- possibly in recognition of the potential for confusion with the subset/superset relation.
The "$\supset$" symbol for implication was originally a backwards "C" and dates back to Peano (1895). He wrote "$pCq$" for "p is a Consequence of q", and also reversed it to "$q\supset p$ for "q has p as a consequence".
According to some sources, writing "$\subset$" (first used by Schröder, 1890) for "is a subset of" replaced earlier use of "$<$" when authors felt set operations ought to be distinguished from the arithmetic notation that was first used by analogy.
Others claim that "$\subset$" dates back to J. Gergonne (1817) who used "C" for "Contained in".
(Most of the above information is from Earliest Uses of Various Mathematical Symbols by Jeff Miller).