For each of the properties reflexive, symmetric, antisymmetric,and transitive, carry out the following.
Assume that R and S are nonempty relations on a set A that bothhave the property. For each of R complement (Rc), R?S, R?Sand R?1.determine whether the new relation
- must also have that property;
- might have that property, but might not; or
- cannot have that property.
Any time you answer Statement i or Statement iii, outline aproof. Any time you answer Statement ii, provide two examples: onewhere the new relation has the property, and one where the newrelation does not.
