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.

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