Questions of various cognitie levels

#1.  Tell if the following relation R is (1) a function (2) injective (3) surjective:
      
       R maps [3] into [3]. R={(1,2),(1,3),(2,2),(3,1)}.




#2.   Create a relation for each given set of characteristics. You may create any sets you like, and they can be different for each relation.


        Function   Injective   Surjective
            Y                Y               Y
            Y                Y               N
            Y                N              Y
            Y                N              N
            N               Y               Y
            N               Y               N
            N               N               Y
            N               N               N




I believe question #1 requires lower-level thinking skills than question #2. Once a person has remembered the definitions of all the terms and understood what they mean, it is fairly straightforward to apply the knowledge to answer the question. I therefore would classify this as a third level problem.


Question #2 requires a bit more.  In addition to the first three levels of remembering, understanding, and applying, students now have to engage in the sixth level of creation. They have to use the knowledge they have learned to create their own original structures. Their creation will form a structured, coherent picture of all possible combinations of the characteristics of relations they have been studying. Creating a relation to match each of the three characteristics simultaneously is surely a higher level thinking skill that involves creativity in addition to merely memorizing, understanding, and applying the knowledge.