Transitivity (mathematics) facts for kids

Transitivity is a cool idea in logic and mathematics. It describes a special rule that some connections, or "relations," follow. Think of it like a chain reaction!

What is Transitivity?

Imagine you have three things: A, B, and C. A relation is transitive if this rule is true:

• If A is connected to B,
• AND B is connected to C,
• THEN A must also be connected to C.

It's like saying if you can get from A to B, and from B to C, then you can definitely get from A to C!

Everyday Examples of Transitivity

Many things we see every day are transitive. Here are some easy examples:

• Being Taller Than: If Alex is taller than Ben, and Ben is taller than Chris, then Alex is definitely taller than Chris. This is a transitive relation.

• Being Bigger Than: If a dog is bigger than a cat, and a cat is bigger than a mouse, then the dog is bigger than the mouse. This also shows transitivity.

• Being a Subset Of: In math, a subset means one group is completely inside another. If Group A is a subset of Group B, and Group B is a subset of Group C, then Group A is also a subset of Group C.

When a Relation is NOT Transitive

Not all connections follow this chain rule. When a relation is not transitive, we call it an intransitive relation.

• Rock, Paper, Scissors: This game is a great example of an intransitive relation.
  • Rock beats scissors.
  • Scissors beats paper.
  • BUT, rock does NOT beat paper (paper beats rock!).
• Because the chain breaks (rock beats scissors, scissors beats paper, but rock doesn't beat paper), this game is intransitive.

Transitivity helps us understand how different things connect and how those connections can lead to new conclusions.

Related pages

• Symmetric relation

See also

In Spanish: Relación transitiva para niños