- #1

kingstar

- 38

- 0

## Homework Statement

a) Consider the relation S defiend on the set {t : t is a person} such that xSy holds exactly if

person x is taller than y. Determine if the relation S is reflexive, symmetric and transitive.

Is the relation S an equivalence relation?

## Homework Equations

Recall that a relation R dened on a set A is reflexive if for all x 2 A xRx.

Recall that a relation R dened on a set A is symmetric if for all x 2 A and y 2 A the xRy implies

yRx.

Recall that a relation R ened on a set A is transitive if for all x; y; z in A, both xRy and yRz

holds, then xRz holds as well.

Finally recall that a relation R is an equivalence relation if its reflexive, symmetric and transitive.

## The Attempt at a Solution

As far as i can see the set is not symmetric or reflexive but I'm not 100% on transitive...

It would be transitive if x > y and y > z then x > z holds...but we aren't given any information on y > z?

So would this set be transitive?