Here's a breakdown:
* Relation: A relationship between two things. This relationship can be anything like "is equal to", "is greater than", "is a friend of", or any other type of connection.
* Transitive: A relation is transitive if the property above holds true.
Examples:
* Equality: If a = b and b = c, then a = c.
* Less than: If a < b and b < c, then a < c.
* Friendship: If A is a friend of B and B is a friend of C, then A is a friend of C (assuming friendship is a transitive relationship).
Non-Examples:
* "Is taller than": If A is taller than B and B is taller than C, it doesn't necessarily mean A is taller than C.
* "Is a parent of": If A is a parent of B and B is a parent of C, then A is a grandparent of C, not a parent.
In short, the transitive property allows us to make inferences about relationships based on existing relationships within a set. It's a fundamental concept in logic and mathematics.