Composition of Binary Relations in Sets

number of elements

7

new relations

R

S

composition R ∘ S

union R ⋃ S

intersection R ⋂ S

none

Given two binary asymmetric relations

R

(red arrows) and

S

(green arrows), this Demonstration shows their composition

R◦S

(dashed blue), union

R⋃S

(dashed brown) and intersection

R⋂S

(dashed black).

The composition of two binary relations is defined by:

x(R◦S)y⇔∃z(xRz∧zSy)

.

[1] E. J. Borowski and J. M. Borwein, The HarperCollins Dictionary of Mathematics, New York: HarperPerennial, 1991 p. 489.

Izidor Hafner