Part Two 317in set C. The six points in set B represent all the elements in that set, and the five elements in
setC represent all the elements of that set. As before, the dashed curves represent the entire
mapping. Is this new mapping a surjection? Is it an injection? Is it a bijection? Is it a relation?
Is it a function?
Answer 13-9
The mapping of Fig. 20-2 is a surjection, because it maps to every element of set C. It’s not an
injection, however, because it’s not one-to-one. That means it is not a bijection. This mapping
is a relation. It’s also a function, because no single element in set B maps to more than one
element in set C.
Question 13-10
Consider the mapping of Fig. 20-2 as a relation. Now suppose the sense were reversed, so that
the mapping went from set C to set B, giving us the inverse of the relation. Would that inverse
be a function?
Answer 13-10
No, because one of the elements of set C would map to two elements of set B.
Chapter 14
Question 14-1
The Cartesian plane is divided into four quadrants. How are those quadrants normally oriented?
How are the positive and negative values of the variables portrayed in those quadrants?
ABCDFigure 20-2 Illustration for Questions and Answers 13-9
and 13-10.