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