Transitivity (mathematics)

binary relation R with the property that xRy and yRz implies xRz

Transitivity is a term in logic and mathematics.


In general, in a set, if a is related to b and b is related to c, then a is related to c.

  • If A>B and B>C, then A>C. Size is transitive.
  • If A is a subset of B and B is a subset of C, then A is a subset of C. Subsets are transitive.
  • If Sidney is taller than Casey, and Casey is taller than Jordan, then we know that Sidney is taller than Jordan. Height is transitive.
  • Rock beats scissors, and scissors beats paper, but rock doesn't beat paper. Rock, paper, scissors is not transitive: It is intransitive.