DISCRETE MATHEMATICS WITH APPLICATION (
5th Edition
ISBN: 9780357097717
Author: EPP
Publisher: CENGAGE L
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Chapter 11.2, Problem 6ES
To determine
The statement using
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. Given the function f: XY (with X and Y as above) defined as
f(2) = 2, f(4) = 1,
ƒ(6)=3, ƒ(8) = 2,
answer the following questions. Justify your answers.
(a) [4 points] Is f injective?
(b) [4 points] Is f surjective?
(c) [2 points] Is f bijective?
1. Let
15 -14
A
= -10
9
13-12
-8 7
11
15
-14 13 -12
-6 and B =
-10 9 -8 7 -6
5
-4
3 -2
E
5 -4 3 -2 1
Explicitly give the values of A2,3, A1,5, and B1,4-
Is A a 5 x 3 matrix? Explain your answer.
Are A and B (mathematically) equal? Explain your answer.
Given the following set
X = {2, 4, 6, 8} and Y = {1, 2, 3},
explicitly give (e.g., write down the sets with numerical entries) of the outputs of the
following requested set operations:
(a) [2 points] XUY (Union)
(b) [2 points] XY (Intersection)
(c) [3 points] X\Y (Difference)
(d) [3 points] XAY (Symmetric Difference)
Chapter 11 Solutions
DISCRETE MATHEMATICS WITH APPLICATION (
Ch. 11.1 - If f is a real-valued function of a real variable,...Ch. 11.1 - Prob. 2TYCh. 11.1 - Prob. 3TYCh. 11.1 - Prob. 4TYCh. 11.1 - Prob. 5TYCh. 11.1 - Prob. 6TYCh. 11.1 - Prob. 1ESCh. 11.1 - The graph of a function g is shown below. a. Is...Ch. 11.1 - Prob. 3ESCh. 11.1 - Sketch the graphs of the power functions p3 and p4...
Ch. 11.1 - Prob. 5ESCh. 11.1 - Prob. 6ESCh. 11.1 - Prob. 7ESCh. 11.1 - Sketch a graph for each of the functions defined...Ch. 11.1 - Prob. 9ESCh. 11.1 - Prob. 10ESCh. 11.1 - Prob. 11ESCh. 11.1 - Prob. 12ESCh. 11.1 - Prob. 13ESCh. 11.1 - The graph of a function f is shown below. Find the...Ch. 11.1 - Prob. 15ESCh. 11.1 - Prob. 16ESCh. 11.1 - Prob. 17ESCh. 11.1 - Prob. 18ESCh. 11.1 - Prob. 19ESCh. 11.1 - Prob. 20ESCh. 11.1 - Prob. 21ESCh. 11.1 - Prob. 22ESCh. 11.1 - Prob. 23ESCh. 11.1 - Prob. 24ESCh. 11.1 - Prob. 25ESCh. 11.1 - Prob. 26ESCh. 11.1 - Prob. 27ESCh. 11.1 - Prob. 28ESCh. 11.2 - A sentence of the form Ag(n)f(n) for every na...Ch. 11.2 - Prob. 2TYCh. 11.2 - Prob. 3TYCh. 11.2 - When n1,n n2 and n2 n5__________.Ch. 11.2 - Prob. 5TYCh. 11.2 - Prob. 6TYCh. 11.2 - Prob. 1ESCh. 11.2 - Prob. 2ESCh. 11.2 - The following is a formal definition for ...Ch. 11.2 - In 4—9, express each statement using -, O-, or ...Ch. 11.2 - In 4—9, express each statement using -, O-, or ...Ch. 11.2 - Prob. 6ESCh. 11.2 - Prob. 7ESCh. 11.2 - Prob. 8ESCh. 11.2 - Prob. 9ESCh. 11.2 - Prob. 10ESCh. 11.2 - Prob. 11ESCh. 11.2 - Prob. 12ESCh. 11.2 - Prob. 13ESCh. 11.2 - Use the definition of -notation to show that...Ch. 11.2 - Prob. 15ESCh. 11.2 - Prob. 16ESCh. 11.2 - Prob. 17ESCh. 11.2 - Prob. 18ESCh. 11.2 - Prob. 19ESCh. 11.2 - Prob. 20ESCh. 11.2 - Prove Theorem 11.2.4: If f is a real-valued...Ch. 11.2 - Prob. 22ESCh. 11.2 - Prob. 23ESCh. 11.2 - a. Use one of the methods of Example 11.2.4 to...Ch. 11.2 - Suppose P(n)=amnm+am1nm1++a2n2+a1n+a0 , where all...Ch. 11.2 - Prob. 26ESCh. 11.2 - Prob. 27ESCh. 11.2 - Prob. 28ESCh. 11.2 - Use the theorem on polynomial orders to prove each...Ch. 11.2 - Prob. 30ESCh. 11.2 - Prob. 31ESCh. 11.2 - Prob. 32ESCh. 11.2 - Prove each of the statements in 32—39. Use the...Ch. 11.2 - Prob. 34ESCh. 11.2 - Prob. 35ESCh. 11.2 - Prob. 36ESCh. 11.2 - Prob. 37ESCh. 11.2 - Prob. 38ESCh. 11.2 - Prob. 39ESCh. 11.2 - Prob. 40ESCh. 11.2 - Prob. 41ESCh. 11.2 - Prob. 42ESCh. 11.2 - Prob. 43ESCh. 11.2 - Prob. 44ESCh. 11.2 - Prob. 45ESCh. 11.2 - Prob. 46ESCh. 11.2 - Prob. 47ESCh. 11.2 - Prob. 48ESCh. 11.2 - Prob. 49ESCh. 11.2 - Prob. 50ESCh. 11.2 - Prob. 51ESCh. 11.3 - When an algorithm segment contains a nested...Ch. 11.3 - Prob. 2TYCh. 11.3 - Prob. 3TYCh. 11.3 - Suppose a computer takes 1 nanosecond ( =109...Ch. 11.3 - Prob. 2ESCh. 11.3 - Prob. 3ESCh. 11.3 - Exercises 4—5 explore the fact that for relatively...Ch. 11.3 - Prob. 5ESCh. 11.3 - Prob. 6ESCh. 11.3 - Prob. 7ESCh. 11.3 - Prob. 8ESCh. 11.3 - Prob. 9ESCh. 11.3 - For each of the algorithm segments in 6—19, assume...Ch. 11.3 - For each of the algorithm segments in 6—19, assume...Ch. 11.3 - For each of the algorithm segments in 6—19, assume...Ch. 11.3 - Prob. 13ESCh. 11.3 - Prob. 14ESCh. 11.3 - For each of the algorithm segments in 6—19, assume...Ch. 11.3 - Prob. 16ESCh. 11.3 - For each of the algorithm segments in 6—19, assume...Ch. 11.3 - Prob. 18ESCh. 11.3 - Prob. 19ESCh. 11.3 - Prob. 20ESCh. 11.3 - Prob. 21ESCh. 11.3 - Construct a trace table showing the action of...Ch. 11.3 - Construct a trace table showing the action of...Ch. 11.3 - Prob. 24ESCh. 11.3 - Prob. 25ESCh. 11.3 - Prob. 26ESCh. 11.3 - Consider the recurrence relation that arose in...Ch. 11.3 - Prob. 28ESCh. 11.3 - Prob. 29ESCh. 11.3 - Exercises 28—35 refer to selection sort, which is...Ch. 11.3 - Prob. 31ESCh. 11.3 - Prob. 32ESCh. 11.3 - Prob. 33ESCh. 11.3 - Prob. 34ESCh. 11.3 - Prob. 35ESCh. 11.3 - Prob. 36ESCh. 11.3 - Prob. 37ESCh. 11.3 - Prob. 38ESCh. 11.3 - Prob. 39ESCh. 11.3 - Prob. 40ESCh. 11.3 - Prob. 41ESCh. 11.3 - Exercises 40—43 refer to another algorithm, known...Ch. 11.3 - Prob. 43ESCh. 11.4 - The domain of any exponential function is , and...Ch. 11.4 - Prob. 2TYCh. 11.4 - Prob. 3TYCh. 11.4 - Prob. 4TYCh. 11.4 - Prob. 5TYCh. 11.4 - Graph each function defined in 1-8. 1. f(x)=3x for...Ch. 11.4 - Prob. 2ESCh. 11.4 - Prob. 3ESCh. 11.4 - Prob. 4ESCh. 11.4 - Prob. 5ESCh. 11.4 - Prob. 6ESCh. 11.4 - Prob. 7ESCh. 11.4 - Prob. 8ESCh. 11.4 - Prob. 9ESCh. 11.4 - Prob. 10ESCh. 11.4 - Prob. 11ESCh. 11.4 - Prob. 12ESCh. 11.4 - Prob. 13ESCh. 11.4 - Prob. 14ESCh. 11.4 - Prob. 15ESCh. 11.4 - Prob. 16ESCh. 11.4 - Prob. 17ESCh. 11.4 - Prob. 18ESCh. 11.4 - Prob. 19ESCh. 11.4 - Prob. 20ESCh. 11.4 - Prob. 21ESCh. 11.4 - Prob. 22ESCh. 11.4 - Prob. 23ESCh. 11.4 - Prob. 24ESCh. 11.4 - Prob. 25ESCh. 11.4 - Prob. 26ESCh. 11.4 - Prob. 27ESCh. 11.4 - Prob. 28ESCh. 11.4 - Prob. 29ESCh. 11.4 - Prob. 30ESCh. 11.4 - Prob. 31ESCh. 11.4 - Prob. 32ESCh. 11.4 - Prove each of the statements in 32—37, assuming n...Ch. 11.4 - Prob. 34ESCh. 11.4 - Prob. 35ESCh. 11.4 - Prob. 36ESCh. 11.4 - Prob. 37ESCh. 11.4 - Prob. 38ESCh. 11.4 - Prob. 39ESCh. 11.4 - Prob. 40ESCh. 11.4 - Show that log2n is (log2n) .Ch. 11.4 - Prob. 42ESCh. 11.4 - Prob. 43ESCh. 11.4 - Prob. 44ESCh. 11.4 - Prob. 45ESCh. 11.4 - Prob. 46ESCh. 11.4 - Prob. 47ESCh. 11.4 - Prob. 48ESCh. 11.4 - Prob. 49ESCh. 11.4 - Prob. 50ESCh. 11.4 - Prob. 51ESCh. 11.5 - Prob. 1TYCh. 11.5 - To search an array using the binary search...Ch. 11.5 - Prob. 3TYCh. 11.5 - Prob. 4TYCh. 11.5 - The worst-case order of the merge sort algorithm...Ch. 11.5 - Prob. 1ESCh. 11.5 - Prob. 2ESCh. 11.5 - Prob. 3ESCh. 11.5 - Prob. 4ESCh. 11.5 - In 5 and 6, trace the action of the binary search...Ch. 11.5 - Prob. 6ESCh. 11.5 - Prob. 7ESCh. 11.5 - Prob. 8ESCh. 11.5 - Prob. 9ESCh. 11.5 - Prob. 10ESCh. 11.5 - Prob. 11ESCh. 11.5 - Prob. 12ESCh. 11.5 - Prob. 13ESCh. 11.5 - Prob. 14ESCh. 11.5 - Prob. 15ESCh. 11.5 - Prob. 16ESCh. 11.5 - Trace the modified binary search algorithm for the...Ch. 11.5 - Prob. 18ESCh. 11.5 - Prob. 19ESCh. 11.5 - Prob. 20ESCh. 11.5 - Prob. 21ESCh. 11.5 - Prob. 22ESCh. 11.5 - Prob. 23ESCh. 11.5 - Show that given an array a[bot],a[bot+1],,a[top]of...Ch. 11.5 - Prob. 25ESCh. 11.5 - Prob. 26ES
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