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Discrete Mathematics and its Applications

Kenneth H. Rosen

$Math Studyset Vaia Explanations$ Math

7th Edition · 808 pages

ISBN: 9780073383095

Chapter 2: Q17E (page 115)

Question: Consider these functions from the set of students in a discrete mathematics class. Under what conditions is the function one-to-one if it assigns to a teacher his or her
Office
Assigned bus to chaperone in a group of buses taking students on a field trip
Salary
Social security number

Short Answer

Expert verified

Answer:

Depends on whether teachers share offices.
One-to-one assuming only one teacher per bus.
Most likely not one-to-one, especially if salary is set by a collective bargaining agreement
One-to-one

Step by step solution

01

Step: 1

Depends on whether teachers share offices.
One-to-one assuming only one teacher per bus.
Most likely not one-to-one, especially if salary is set by a collective bargaining agreement
One-to-one

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Most popular questions from this chapter

Show that when you substitute ${(3 n + 1)}^{2}$ for each occurrence of n and ${(3 m + 1)}^{2}$ for each occurrence of m in the right-hand side of the formula for the function $f (m, n)$ in Exercise 31 , you obtain a one-to-one polynomial function $Z \times Z \to Z$ . It is an open question whether there is a one-to-one polynomial function $Q \times Q \to Q$ .

Consider these functions from the set of students in a discrete mathematics class. Under what conditions is the function one-to-one if it assigns to a teacher his or her

Office
Assigned bus to chaperone in a group of buses taking students on a field trip
Salary
Social security number

Question: Suppose that g is a function from A to B and f is a function from B to C.

a) Show that if both f and g are one-to-one functions, then $f \circ g$ is also one-to-one. b) Show that if both f and g are onto functions, then $f \circ g$ is also onto.

Construct a truth table for each of these compound propositions.

a. $(p \lor q) \to (p \oplus q)$

b.. $(p \oplus q) \to (p \land q)$

c. $(p \lor q) \oplus (p \land q)$

d. $(p \leftrightarrow q) \oplus (\neg p \leftrightarrow q)$

e. $(p \leftrightarrow q) \oplus (\neg p \leftrightarrow \neg r)$

f. $(p \oplus q) \to (p \oplus \neg q)$

Compute each of these double sums

$\begin{aligned} \sum_{i = 1}^{3} \sum_{j = 1}^{2} (i - j) \\ \sum_{i = 0}^{3} \sum_{j = 0}^{2} (3 i + 2 j) \\ \sum_{i = 1}^{3} \sum_{j = 0}^{2} j \\ \sum_{i = 0}^{2} \sum_{j = 0}^{3} i^{2} j^{3} \end{aligned}$

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