316 Review Questions and Answers
Answer 13-4
The mapping is a bijection between B and C, because it is both a surjection and an
injection.Question 13-5
Based on Fig. 20-1, and on the descriptions given so far, what type of relation is the mapping
between B and C?Answer 13-5
The mapping is a function, because no single element in set B is mapped to more than one
element in set C.Question 13-6
Suppose the sense of the mapping in Fig. 20-1 were reversed, so that it went from set C to
setB. This would give us the inverse of the relation from B to C. Would that inverse be a
function?Answer 13-6
Yes, because no single element in set C would map to more than one element in set B.Question 13-7
Let’s call the five points in set B of Fig. 20-1 by the names b 1 through b 5 , and the five points in
setC by the names c 1 through c 5. Suppose that b 1 maps to c 5 ,b 2 maps to c 4 ,b 3 maps to c 3 ,
b 4 maps to c 2 , and b 5 maps to c 1. How can we state this mapping as a set of ordered pairs?Answer 13-7
We can state the mapping as the set{(b 1 ,c 5 ), (b 2 ,c 4 ), (b 3 ,c 3 ), (b 4 ,c 2 ), (b 5 ,c 1 )}Question 13-8
In the ordered pairs given in Answer 13-7 relevant to Fig. 20-1, which elements are values of
the independent variable? Which elements are values of the dependent variable?Answer 13-8
The elements b 1 through b 5 are values of the independent variable, and the elements c 1 through
c 5 are values of the dependent variable.Question 13-9
Figure 20-2 shows a mapping that’s almost the same as the mapping of Fig. 20-1. The only
difference is that there is an extra element in set B, and it maps to one of the existing elements