Mathematical Relations: possible to be not refl., trans., or

[barra]

Is it possible to have a relationship that is not reflexive, transitive or symmetric? If someone is able to find an example it would be greatly appreciated.

Thanks Barra

 

[stapel]

Is it possible to have a relationship that is not reflexive, transitive or symmetric?

What does it mean for a relation to be "reflexive"? What examples did your book and / or instructor give for "reflexive" and "not reflexive"?

What does it mean for a relation to be "transitive"? What examples did your book and / or instructor give for "transitive" and "not transitive"?

What does it mean for a relation to be "symmetric"? What examples did your book and / or instructor give for "symmetric" and "not symmetric"?

What are your thoughts?

 

[barra]

the defintions I have been given are:

reflexive - a relation is reflexive if each element in the set is related to itself.

symmetric - a relation is symmetric if element b is related to element a whenever a is related to b.

transitive - a realtion is transitive if, given that a is related to b and b is related to c, it is necessarily true that a is related to c.

The example i have been given is, in the set of integers with the relation a is related to b if a divides b, the realtion is reflexive because a / a (why is this reflexive??). The relation is not symmetric because it is not necessarily true that a/b implies b/a. It is transitive becasue when a divides b and b divides c, it is always true that a divides c (where does c come from?).

thanks