Question

Let A =
(1,2,3,4). Find a relation R on A such that: R is reflexive neither antisymmetric nor symmetric

Answer 1

reflexive means (x,x) is in it for every x

Answer 2

so you know you need \(\{(1,1).(2.2),(3,3),(4,4)\}\)

Answer 3

the relation above however is anti-symmetric since it is the case that if
\((x,y)\in R\) then x = y so i think you need only add one more maybe use \(\leq \)

Answer 4

maybe i am making this harder than it is. why not just add two more
\[\{(1,1).(2.2),(3,3),(4,4),(1,2),(2,3),(3,2)\}\]

Answer 5

it is reflexive. it is not symmetric because you have (1,2) but not (2,1) and it is not anti symmetric because you have (2,3) and (3,2) but \(2\neq 3\)

Answer 6

does that look reasonable?

Answer 7

Ok I understand it much better now.

Answer 8

good. glad it helped