Let and
be two events of an experiment.
Given a statement:
implies
but
does not imply
(or simply
implies
).
e.g.
A: Otaku.
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:
and
.
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Gaia disagree with my misuse of Mathematics notation.