Question

Let R={(1,5),(2,2),(3,4)(5,2)} S={(2,4),(3,4),(3,1),(5,5)} Find:

Answer 1

R dot S

Answer 2

\[R\circ S\] right?

Answer 3

Yes

Answer 4

first we do \(S\), then we do \(R\)
lets go slow

Answer 5

what is \(S(2)\)?

Answer 6

for that you need to look here
\[S=\{(2,4),(3,4),(3,1),(5,5)\}\]

Answer 7

ok so that is 2,4

Answer 8

you see the "ordered pair" \((2,4)\) so \(S(2)=4\) i.e. \(S\) sends \(2\) to \(4\)

Answer 9

okay

Answer 10

then what does \(R\) do to \(4\)?

Answer 11

R sends it to 3?

Answer 12

no not quite
do you see any ordered pair in \(R\) where the first number is \(4\) ?

Answer 13

no

Answer 14

neither do i
so \(R\) does not have \(4\) in its domain, so
\[R\circ S\] does not have \(2\) in its domain
skip that one, lets move on

Answer 15

ok so if it is s(3) then that sends it to 4 which i also see none in R
but if i see s(3) then it sends to 1 so then in R 1 is sending it to 5 then my answer would be (1,5)

Answer 16

yes exactly

Answer 17

oh no hold on!

Answer 18

ok so then the last one would be s(5) sends to 5 then on R 5 sends to 2 so then my answer is (5,2)?

Answer 19

you wrote \but if i see s(3) then it sends to 1 so then in R 1 is sending it to 5 then my answer would be (1,5)
which is almost right except for the last line

Answer 20

so then i switch?

Answer 21

S sends 3 to 1
R sends 1 to 5
so \(R\circ S\) sends 3 to 5
ordered pair is \((3,5)\)

Answer 22

okay

Answer 23

i think i go it

Answer 24

got*

Answer 25

also \(S\) sends 5 to 5, and \(R\) sends 5 to 2 so \(R\circ S\) sends 5 to 2
ordered pair is \((5,2)\)

Answer 26

and those are the only ordered pairs for \(R\circ S\)
you got it? do you have another one to do?

Answer 27

and if it was S dot Rwould i start with R?

Answer 28

yes

Answer 29

Yes i have another let me work it out and ill give you my answers

Answer 30

ok i will do S dot R

Answer 31

kk

Answer 32

ok and while you do it i will copy it down here so i don't have to keep scrolling up
Let \(R=\{(1,5),(2,2),(3,4)(5,2)\} ,S=\{(2,4),(3,4),(3,1),(5,5)\} \)

Answer 33

ok I got (2,4), (4,1) (4,4), (2,5)

Answer 34

is that for \(S\circ R\)?

Answer 35

yes

Answer 36

ok then we better go slow

Answer 37

okay

Answer 38

the first ordered pair i see in \(R\) is \((1,5)\) meaning \(R\) send \(1\) to \(5\)
so we start with \((1,?)\)

Answer 39

then ask what does \(S\) do with \(5\)?

Answer 40

sends to 5

Answer 41

k good
so the first ordered pair of \(S\circ R\) is \((1,5)\)

Answer 42

okay

Answer 43

the next ordered pair i see in \(R\) is \((2,2)\) meaning \(R\) sends 2 to 2
now we write \((2,?)\)
what does \(S\) do with \(2\) ?

Answer 44

sends to 4

Answer 45

ok so what is the ordered pair for \(S\circ R\) that starts \((2,?)\) ?

Answer 46

2,4

Answer 47

got it
now on to the next one

Answer 48

the next one is none

Answer 49

i see \((3,4)\) meaning... right none
so we don't include a pair starting at 3

Answer 50

(5,4) for the last?

Answer 51

yes

Answer 52

you see you are just chasing through the ordered pairs
important to know which one comes first is all

Answer 53

Ok it makes much mored send i just have to take it slow thank you you for explaining

Answer 54

yw, hope it is more or less clear

Answer 55

sense*

Answer 56

thank you

Answer 57

i like "mored send" too

Answer 58

lol thanks im gonna get back to doing the other problems