Transitive relation

[dull nimbus]

whats a transitive relation?
if a , b E r and b, c E r then a , c E r ?

why it says missing cases for
The set X={1,2,3,4},
R ={(1,1),(1,2),(2,1)}

[amber fiber]

send full question

[dull nimbus]

there is a set X and a relation R i have to determine
whether the relation is
1.) Reflexive
2.) Symmetric
3.) Transitive

[gusty cosmos]

A transitive relation is one where if you have elements (a,b) and (b,c), then you must necessarily have (a,c) too.
For example, consider the relation of equality. If a = b, b = c, then a = c. Thus this relation is transitive

[dull nimbus]

R ={(1,1),(1,2),(2,1)}

acc to this rule
relation is transitive

ive 1->2 , 2->1 and 1->1

so its transitive

[gusty cosmos]

Yeah but does it apply to all

[dull nimbus]

having all the pairs is necessary or not?

[gusty cosmos]

I mean my maths teacher sure did say it was necessary

We did this too at the start of the year

Yea its for all

[dull nimbus]

is it like
if a,b E r and b,a E r
then a,c E r

or

a,b must E r and b,a must E r
then a,c E r

[gusty cosmos]

(a,b E r), (b,c E r), (a,c E r)

Like take a relation of ewuality

x = y, y = z then x = z. So this relation is transitive

You can take any variable in (x,y,z)

[dull nimbus]

whats the meaning of missing cases here

why its not transitive

[gusty cosmos]

You have (1,1),(1,2) (a = 1, b = 1, c = 2) transitivity requires (a,c) i.e. (1,2)

[dull nimbus]

basically
a!=c

?

[gusty cosmos]

Uh

You need (1,2) for transitivitu

[dull nimbus]

i got it i dont have 2,2

ive 2-> 1 and 1 -> 2

but not 2 -> 2

thanks, i appreciate the support ^^