Definition 5.6 (Inverse Relation)
R~: Y X is defined as { (y,x) | (x,y) R }.
Consequently, xRy yR~x
Definition 5.7 (Composition of R and S)
Consequently:
x(R O S)z it exists y with xRy and yRz
Examples:
Let R be the relation x has a friend y and let S be the relation y owns a motorbike.
Find the relation R O S.
R: x has a friend y
Solution:
R: { (x,y) | x has a friend y } and x,y { A, B, C, D, E } =
{ (A,B), (A,D), (B,C), (C,E) }
S: { (x,m) | y owns a motorbike } and x { A, B, C, D } and m { Speedy and Slow } =
{ (C, Speedy), (E, Slow) }
So we know: R O S = { (B, Speedy), (C, Slow) }
A graphically representation of the composition board
If x has a friend y means also y has a friend x. Calculate: R O S
Definition 5.8 (Associative Operations)
( R O S ) O P = R ( S O P )
Examples:
Last modified: 27/July/98 (12:14)