This is not correct...if aRb then bRa only if a=b this means antisymmetric

You're correct that your statement refers to the definition of an antisymmetric relation. Here's a clarification:

A relation \( R \) on a set \( A \) is **antisymmetric** if for all \( a, b \in A \), whenever both \( aRb \) and \( bRa \) hold, it must be that \( a = b \).

- **Formally**: \( R \) is antisymmetric if \(\forall a, b \in A\), \((aRb \land bRa) \implies a = b\).

This means that if \( a \) is related to \( b \) and \( b \) is related to \( a \), then \( a \) and \( b \) must be the same element. In simpler terms, in an antisymmetric relation, the only way two different elements can be related in both directions is if they are actually the same element.

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Here are 8 related questions to expand on this information:

1. What is the difference between symmetric and antisymmetric relations?
2. Can a relation be both symmetric and antisymmetric? If so, under what conditions?
3. How does antisymmetry differ from asymmetry in relations?
4. Can you provide an example of an antisymmetric relation?
5. What is the role of antisymmetry in partial orders?
6. How does antisymmetry relate to reflexivity?
7. What are some real-world examples of antisymmetric relations?
8. How does antisymmetry influence the properties of equivalence relations?

**Tip:** When analyzing relations, it's important to distinguish between properties like reflexivity, symmetry, antisymmetry, and transitivity to fully understand the nature of the relation.

Explore the concept of antisymmetric relations in mathematics. Learn about the definition, properties, and examples of antisymmetric relations. This page provides a detailed explanation with examples and related questions.

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