Math 301                                                                                                                         Name:
Quiz 5

  1. Let $R$ be the relation on MATH (i.e., the set of nonzero integers) defined by $_{x}R_{y}$ if $x=-y.$ For each of the five properties of relations, determine if this relation has the property and prove your assertion (with either a proof or a counterexample as appropriate.) Note: Make sure your work is done in an organized and neat fashion. It will not receive credit if it is not easily and clearly understandable.



 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 
 

  1. Let MATH Give an example of a relation $R$ on $A$ that is transitive, but neither symmetric nor reflexive.