Question

Let A={1,2,3,4,5,6}* {1,2,3,4,5,6} and define a relation R on A as follows:
For (a,b),(c,d)ϵA, (a,b)R(c,d) if and only if ab=cd.
(i) Verify that R is an equivalence relation on A.
(ii) Determine the equivalence class [(2,3)].

Help me pls~ i really duno how to do it~

Answer 1

it is \(A=\{1,2,3,4,5,6\}\times \{1,2,3,4,5,6\}\)

Answer 2

ya~ is A={1,2,3,4,5,6}×{1,2,3,4,5,6}

Answer 3

is the relation given by \((a,b)R(c,d)\iff ad=bc\)

Answer 4

yes

Answer 5

not what you wrote, right? what i wrote

Answer 6

\(ad=bc\) defines the relation, right?

Answer 7

no~ is ab=cd~

Answer 8

ok

Answer 9

for example \((2,6)R(4,3)\)

Answer 10

because \(2\times 6=4\times 3\)

Answer 11

so you have to show that this relation is
Reflexive,
Symmetric
Transitive

do you know what these mean and how to do it?

Answer 12

i am just wondering. if you do not, that if fine i can try to explain

Answer 13

ok~ the reflexive, symmetric and transitive i know how to do it~ how about the (ii)?
bcz i don't the question asking what.

Answer 14

that is the easy part!!

Answer 15

if you have an equivalence relation \(\equiv\) then it is like having an equal sign
what you have to do is find all the pairs that are in the equivalence class of \((2,3)\) that is all pairs \((c,d)\) such that \(c\times d=2\times 3=6\)

Answer 16

for example \((6,1)\) is in that equivalence class, since \(6\times 1=6\)

Answer 17

i think there are exactly 4 ordered pairs in that class
does this make sense? you did all the hard work if you proved the rst part

Answer 18

oh~ i get what you mean~ okok~ thx~~ =D

Answer 19

yw
good luck
for further understanding, find all the equivalence classes. it is not hard