[Verse 1]
In the kingdom of relations, four guardians stand
Reflexive whispers "every element holds its own hand"
When a relates to a, no exceptions allowed
Like less-than-or-equal, it makes numbers proud
[Chorus]
Reflexive loops back home
Symmetric swaps the throne
Antisymmetric locks it down tight
Transitive builds a bridge through the night
Properties dancing in mathematical space
Each one wearing a different face
[Verse 2]
Symmetric plays the mirror game
If a connects to b, then b does the same
Equality's the perfect friend
What goes one way comes back again
[Chorus]
Reflexive loops back home
Symmetric swaps the throne
Antisymmetric locks it down tight
Transitive builds a bridge through the night
Properties dancing in mathematical space
Each one wearing a different face
[Verse 3]
Antisymmetric guards the gate
If both directions terminate
At the very same location
Then those elements share one foundation
[Bridge]
Transitive builds chains so strong
If a to b and b to c belong
Then a to c must also flow
Like dominoes in a perfect row
[Verse 4]
Don't be fooled by the names they wear
Symmetric and anti can both be there
Equality holds both crowns at once
Relations break our simple hunts
[Final Chorus]
Reflexive loops back home
Symmetric swaps the throne
Antisymmetric locks it down tight
Transitive builds a bridge through the night
Four properties in one relation's embrace
Mathematics wearing every face
[Outro]
In the algebra of connections made
These four properties never fade
Check each one with careful eyes
Relations hold such sweet surprise