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The statement "My mother is my parent" is always true, however, the opposite statement "My parent is my mother" is not always true because my father is also my parent.

What's the right term in logic for this phenomenon? And what are the fallacies that overlook this phenomenon called?

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    Another term in logic is TRANSITIVE RELATIONSHIPS. There are theories of relation such as transitive, symmetrical, syncategorematic, etc. – Logikal Oct 26 at 15:22
  • @Logikal - Thank you. Do you happen to have any link talking about these terms? – brilliant Oct 26 at 16:15
  • @Mauro allegranza, perhaps I was not clear. I did not mean the example was indeed transitive. I meant the relationship was in that form. The form would actually be either transitive, intransitive and non transitive. In this context there are three alternatives not just two. I did not want to go too deep into this in a comment. That if one looked into the relationship of transitive one would also find the other variations exist. The OP example would have to be one if the three alternatives and not just two options. People tend to think of non as a not which is not accurate. Here we see that. – Logikal Oct 27 at 11:08
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    @Mauro Allegranza, I see you get where I was coming from now. Sorry if I was not clear. Yes the relationship of x is the Mother of y is a INTRANSITIVE relationship because it works only in one direction. The other direction which is wrong would turn out false. The point I make is that there are THEEE alternatives to many relationships and not two. Most people tend to think a NON is equivalent or equal to NOT. Here we see context where that a NOT can be distinguished from the prefix NON without dispute. The relationship transitive, symmetric and reflective all have three alternatives. – Logikal Oct 27 at 11:25
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    @Brilliant, just to be clear I did not MEAN your example was literally TRANSITIVE. I was referring to the category of TRANSITIVITY which has three alternatives. Your specific example is literally INTRANSITIVE because a woman being the MOTHER OF and PARENT OF X is always true but not vice versa. There is only two individuals there. The father of is another possibility which is why the claim the PARENT OF X IS THE MOTHER OF X is false! You don't need three entities necessarily. Three entities is the usual case. There are transitive, intransitive and non transitive relationships to chose from. – Logikal Oct 28 at 14:33
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The difference is that between inclusion and equality.

The set of Mothers of x is included into the set of Parents of x, but not vice versa:

every Mother is a Parent, but not every Parent is a Mother.

In terms of Aristotelian logic, we have that "being a Parent" is predicated of every Mother.

We may also say that the concept Mother is subordinated to the concept Parent.

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6

One could say that being your mother is sufficient, but not necessary for being your parent.

Thus, thus phenomenon could be called "sufficiency" (without necessity).

Fallacies that overlook this are affirming the consequent, in which one infers being your mother based on being your parent, and denying the antecedent, in which one infers not being your parent based on not being your mother.

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In linguistics, the words mother and father are hyponyms to the word parent and parent is a hypernym to mother and to father.
In logic, the proposition x is the mother/father of y entails that x is a parent of y but parenthood does not entail motherhood/fatherhood.

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The simple answer is that motherhood implies parenthood, while parenthood does not imply motherhood.

Or: being a mother implies being a parent, while being a parent does not imply being a mother.

So "implication" is the right term that applies to this relation.

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A quick observation : in the OP's example, the statement "my parent is my mother" is true but not complete.

A false statement would be "my ONLY parent is my mother" - but that was not stated nor does the actually stated form imply that "my parent is my father" cannot also be true as one person (conventionally) has either two parents or is a clone -case in which the team of scientists and the "parent" organisms can be seen as "mother(s)" (?).

Anyway, the pedantic thing to call that could be "assimetry by omission" in which one would adress elements of the subclass "mother/father" in relation to the descriptor in the superclass "parents" that includes it. Generalization by omission, or simply stating parts of complex truths without implying completitude (not a lie by omission), are weaker forms. In extremis there is nothing wrong with the example given from a strictly logical point of view " my mother is my parent" =true, but the other part of the truth " people (usually) have two parents" = also true does not change the first conclusion.

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