Question

How is this a symmetric relation ?

the pairs (1,1),(1,2),(2,1),(1,-1), and (2,2) are given,

Relations:

R1 = {(a,b) such that a<=b }
R2 = {(a,b) such that a>b }
R3 = {(a,b) such that a<=b }
R1 = {(a,b) such that a=b or a=-b }
R4 = {(a,b) such that a=b }
R5 = {(a,b) such that a=1+b }
R6 = {(a,b) such that a+b <=3 }

how is R3,R4 are symmetric ? I already know why R6 is , since we're looking in (1,2),(2,1) which both must be included in the relation

but for example R4 :

a is not equal to b since we're taking both those pairs.

Answer 1

draw them out

Answer 2

wait , shouldn't we take two pairs that could let the relation be a symmetric relation for example (1,2) , (2,1) and then check ?

Answer 3

when I took this course, no one in class knew how to see the symmetric of the relation. My prof got angry, he said: "why? just draw the diagonal line, every thing pop up and no one do it, why " hahahaha...

Answer 4

I don't blame them :D

Answer 5

you have to have at least 2 elements in the group to consider whether the relation is symmetric or not.

Answer 6

and in this case , it's (1,2) , (2,1)

Answer 7

for example, R1 ={(1,1), (2,2), (1,2)} draw them out, if you have (2,1) in the group, then, R1 is symmetric. Unfortunately, you don't have that element because the define is \((a,b)such ~~that~~ a\leq b\)

Answer 8

got me?

Answer 9

you have to do one by one, for example for R2 ={(1,-1) ,(2,1) }draw them out