Algebra Know-It-ALL

Part Two 315

Answer 13-1

The maximal domain is set A. The co-domain is set D. The essential domain is set B. The
range is set C.

Question 13-2

In Fig 20-1, the five points within set C represent the entire set. On that basis, what can we
say about the mapping?

Answer 13-2

The mapping is onto set C. That is, it is a surjection.

Question 13-3

In Fig 20-1, note that each of the points in set B maps to a single point in set C. What can we
say about the mapping on this basis?

Answer 13-3

The mapping is one-to-one. That is, it is an injection.

Question 13-4

In Fig 20-1, suppose that each point in set B maps to a single point in set C, and vice-versa.
On this basis, and according to what we know so far about the points and the sets, what type
of mapping is this?

A

B

C

D

Figure 20-1 Illustration for Questions and Answers 13-1

through 13-8.