Editing Association fallacy (section)

== Formal version ==
[[File:Euler diagram.png|thumb|216x216px|An Euler diagram illustrating the association fallacy]]
Using the language of [[set theory]], the formal fallacy can be written as follows:
:'''Premise:''' A is in set S1
:'''Premise:''' A is in set S2
:'''Premise:''' B is also in set S2
:'''Conclusion:''' Therefore, B is in set S1.

In the notation of [[first-order logic]], this type of fallacy can be expressed as ([[∃]]''x''&nbsp;[[∈]]&nbsp;''S''&nbsp;:&nbsp;''φ''(''x''))&nbsp;⇒&nbsp;([[∀]]''x''&nbsp;∈&nbsp;''S''&nbsp;:&nbsp;''φ''(''x'')).

The fallacy in the argument can be illustrated through the use of an [[Euler diagram]]: A satisfies the requirement that it is part of both sets S1 and S2, but representing this as an Euler diagram makes it clear that B could be in S2 but not S1.