The general idea is

One set is part of a group, but the whole group is not a set

This might be kind of vague but I don't have a better example right now on this other than...

All revolutionaries are terrorists, but not all terrorists are revolutionaries.


I think you are referring to an association fallacy:

  • an inductive informal fallacy of the type hasty generalization or red herring which asserts that qualities of one thing are inherently qualities of another, merely by an irrelevant association.

  • The two types are sometimes referred to as guilt by association and honor by association. Association fallacies are a special case of red herring, and can be based on an appeal to emotion.

A syllogistic example of guilt by association:

  • John is a con artist. John has black hair. Therefore, all people with black hair are con artists.

The logical inverse of "guilt by association" is honor by association where one claims that someone or something must be reputable because of the people or organizations that are related to it or otherwise support it. For example:

  • Citizens of Country X won more Nobel Prizes, gold medals, and literary awards than citizens of Country Y. Therefore, a citizen of Country X is superior to a citizen of Country Y.



Your sentence is like saying :

All cats are mammals, but not all mammals are cats

As you said, we are talking about sets, one set being an element, or member, of the other.

It is described on wikipedia :

The relation "is an element of", also called set membership, is denoted by the symbol "".

By the way, all revolutionaries are not terrorists, cf Gandhi.

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