Let and be two events of an experiment.
Given a statement:
implies but does not imply (or simply implies ).
B: Watch Anime.
That is: Otaku watches Animes. But those who watch Anime may not be an Otaku.
In Set Theory, we may say is inside but is not inside . Or .
To put them into conditional probability:
Thus, the statement: “A implies B but B does not imply A” may be written as:
Gaia disagree with my misuse of Mathematics notation.