Find the Composion of this relation

[Jakes]

A = {1,2,3}
B= {a,b,c}
c = {x,y,z}

R = {(1,a) (2,c) (3,a) (3,c)}
S = {(b,x) (b,z) (c,y)}

Find RoS (composition of relation)my solution was this:
(2,c) belongs to R and (c,y) belongs to S so (2,y) belongs to RoS
(3,c) belongs to R and (c,y) belongs to S so (3,y) belongs to Ros
RoS={(2,y) 3,y}

can we use (c,y) more than one time..
Is this correct answer ??

 

[issacnewton]

i think you are finding the composition relation $S\circ R$ since
R is relation from A to B and S is relation from B to C. So if you are seeking
$S\circ R$ , then your your first two lines are correct but the final answer
is not since you forgot to put brackets for $(3,y)$ .so

$$S\circ R=\{(2,y),(3,y)\}$$

and its ok to use (c,y) more than one time

 

[HallsofIvy]

If you are indeed looking for RoS, then note that S "takes b into" both x and z but there is no pair in R having x or z as a first member. Similarly, S "takes c into" y but there is no pair in R having y as first member. RoS does not exist (or is the empty relation).


To find SoR, R "takes 1 to" a but there is no pair in S with first member a so there is no pair in SoR with first member 1. R "takes 2 to" c and S "takes c to y" so SoR contains (2, y). R "take 3 to" both a and c. There is no pair in S with first member a but S "takes c to" y so (3, y) is in RoS.

 

[Jakes]

Thanks both of you :)

 

[blue_raver22]

Yes, your solution is correct. In a composition of relations, one element from the first set can be paired with multiple elements from the second set. In this case, the element "c" from set B is paired with "y" twice in the composition RoS.