# Binary Relations

• Apr 25th 2011, 07:05 PM
Oiler
Binary Relations
Hey all,

For the following set {a,b,c}, How can I determine if the Relation, R = {(a,a),(a,b),(a,c)} is reflexive, symmetric, antisymmetric or transitive ?

Thanks.
• Apr 25th 2011, 07:32 PM
topsquark
Quote:

Originally Posted by Oiler
Hey all,

For the following set {a,b,c}, How can I determine if the Relation, R = {(a,a),(a,b),(a,c)} is reflexive, symmetric, antisymmetric or transitive ?

Thanks.

Reflexive: For all x we require that x~x

Symmetric: For all x, y that satisfy x~y, that also y~x

Antisymmetric: For all x, y if x~y and y~x then x = y

Transitive: For all x, y, z if x~y and y~z then x~z

In your case, for example, we know that your relation is not reflexive because there is only one element such that x~x. (ie. a~a, but not b~b and c~c.)

-Dan
• Apr 25th 2011, 08:16 PM
Oiler
For the case where it is transitive, would you say: a~b and b~c then a~c, but there's no such b~c so the relation is not transitive ?