WOLFRAM NOTEBOOK

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).

Details

The composition of two binary relations is defined by:
x(R◦S)y⇔∃z(xRz∧zSy)
.

References

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

External Links

Permanent Citation

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