Discrete Mathematics with Graph Theory
3rd Edition
ISBN: 9780131679955
Author: Edgar G. Goodaire
Publisher: Prentice Hall
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Chapter 3.2, Problem 2E
Define
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Solve questions by Course Name (Ordinary Differential Equations II 2)
d((x, y), (z, w)) = |xz|+|yw|, show that whether d is a metric on
R² or not?.
Q3/Let R be a set of real number and d: R² x R² → R such that
->
d((x, y), (z, w)) = max{\x - zl, ly - w} show that whether d is a metric
on R² or not?.
Q4/Let X be a nonempty set and d₁, d₂: XXR are metrics on X let
d3,d4, d5: XX → R such that
d3(x, y) = 4d2(x, y)
d4(x, y) = 3d₁(x, y) +2d2(x, y)
d5(x,y) = 2d₁ (x,y))/ 1+ 2d₂(x, y).
Show that whether d3, d4 and d5 are metric on X or not?
Chapter 3 Solutions
Discrete Mathematics with Graph Theory
Ch. 3.1 - True/False Questions A function from a set A to a...Ch. 3.1 - Prob. 2TFQCh. 3.1 - Prob. 3TFQCh. 3.1 - Prob. 4TFQCh. 3.1 - Prob. 5TFQCh. 3.1 - True/False Questions Define f:ZZ by f(x)=x+2. Then...Ch. 3.1 - Prob. 7TFQCh. 3.1 - Prob. 8TFQCh. 3.1 - Prob. 9TFQCh. 3.1 - Prob. 10TFQ
Ch. 3.1 - Prob. 11TFQCh. 3.1 - Prob. 12TFQCh. 3.1 - Determine whether each of the following relation...Ch. 3.1 - 2. Suppose A is the set of students currently...Ch. 3.1 - Prob. 3ECh. 3.1 - Prob. 4ECh. 3.1 - Prob. 5ECh. 3.1 - Prob. 6ECh. 3.1 - Prob. 7ECh. 3.1 - Prob. 8ECh. 3.1 - Prob. 9ECh. 3.1 - Prob. 10ECh. 3.1 - Prob. 11ECh. 3.1 - Prob. 12ECh. 3.1 - Prob. 13ECh. 3.1 - Define g:ZB by g(x)=|x|+1. Determine (with...Ch. 3.1 - Define f:AA by f(x)=3x+5. Determine (with reasons)...Ch. 3.1 - 16. Define by . Determine (with reasons) whether...Ch. 3.1 - Prob. 17ECh. 3.1 - Prob. 18ECh. 3.1 - Prob. 19ECh. 3.1 - Define f:RR by f(x)=3x3+x. Graph f to determine...Ch. 3.1 - 21. (a) Define by . Graph g to determine whether g...Ch. 3.1 - Prob. 22ECh. 3.1 - 23. Let a, b, c be real numbers and define by ....Ch. 3.1 - 24. For each of the following, find the largest...Ch. 3.1 - Prob. 25ECh. 3.1 - Let S be a set containing the number 5. Let...Ch. 3.1 - Prob. 27ECh. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - Prob. 30ECh. 3.1 - Prob. 31ECh. 3.1 - Prob. 32ECh. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.2 - True/False Questions
The function defines by ...Ch. 3.2 - True/False Questions The function f:ZZ defines by...Ch. 3.2 - Prob. 3TFQCh. 3.2 - Prob. 4TFQCh. 3.2 - Prob. 5TFQCh. 3.2 - Prob. 6TFQCh. 3.2 - Prob. 7TFQCh. 3.2 - Prob. 8TFQCh. 3.2 - Prob. 9TFQCh. 3.2 - Prob. 10TFQCh. 3.2 - Let . Find the inverse of each of the following...Ch. 3.2 - 2. Define by . Find a formula for .
Ch. 3.2 - Define f:(,0][0,) by f(x)=x2. Find a formula for...Ch. 3.2 - 4. Define by . Find a formula for .
Ch. 3.2 - Prob. 5ECh. 3.2 - Prob. 6ECh. 3.2 - Show that each of the following functions f:AH is...Ch. 3.2 - Prob. 8ECh. 3.2 - Prob. 9ECh. 3.2 - Prob. 10ECh. 3.2 - 11. Let and define functions by and . Find
(a) ...Ch. 3.2 - Prob. 12ECh. 3.2 - Prob. 13ECh. 3.2 - Prob. 14ECh. 3.2 - Prob. 15ECh. 3.2 - Prob. 16ECh. 3.2 - 17. Let A denote the set . Let i denote the...Ch. 3.2 - Prob. 18ECh. 3.2 - Prob. 19ECh. 3.2 - Prob. 20ECh. 3.2 - Prob. 21ECh. 3.2 - Prob. 22ECh. 3.2 - Prob. 23ECh. 3.2 - Prob. 24ECh. 3.2 - Is the composition of two bijective functions...Ch. 3.2 - 26. Define by .
(a) Find the values of .
(b) Guess...Ch. 3.2 - Prob. 27ECh. 3.2 - Prob. 28ECh. 3.3 - True/False Questions
If sets A and B are in...Ch. 3.3 - Prob. 2TFQCh. 3.3 - Prob. 3TFQCh. 3.3 - Prob. 4TFQCh. 3.3 - True/False Questions If A and B are finite sets...Ch. 3.3 - True/False Questions If the conditions of...Ch. 3.3 - Prob. 7TFQCh. 3.3 - Prob. 8TFQCh. 3.3 - Prob. 9TFQCh. 3.3 - Prob. 10TFQCh. 3.3 - Prob. 1ECh. 3.3 - At first glance, the perfect squares 1, 4, 9, 16,...Ch. 3.3 - Prob. 3ECh. 3.3 - Prob. 4ECh. 3.3 - Prob. 5ECh. 3.3 - Prob. 6ECh. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.3 - Prob. 9ECh. 3.3 - Prob. 10ECh. 3.3 - Prove that the notion of same cardinality is an...Ch. 3.3 - Prob. 12ECh. 3.3 - Prob. 13ECh. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Prob. 16ECh. 3.3 - Prob. 17ECh. 3.3 - Prob. 18ECh. 3.3 - Prob. 19ECh. 3.3 - Prob. 20ECh. 3.3 - Prob. 21ECh. 3.3 - 22. Given an example of each of the following or...Ch. 3.3 - Prob. 23ECh. 3.3 - Prob. 24ECh. 3.3 - Prove that the points of a plane and the points of...Ch. 3.3 - Prob. 26ECh. 3.3 - 27. (a) Show that if A and B are countable sets...Ch. 3.3 - Prob. 28ECh. 3.3 - 29. Let S be the set of all real numbers in the...Ch. 3.3 - Let S be the set of all real numbers in the...Ch. 3.3 - Prob. 31ECh. 3 - Define by . Determine whether f is one-to-one.
Ch. 3 - Let f={(1,2),(2,3),(3,4),(4,1)} and...Ch. 3 - Prob. 3RECh. 3 - Prob. 4RECh. 3 -
5. Answer these questions for each of the given...Ch. 3 - Prob. 6RECh. 3 - Prob. 7RECh. 3 - Prob. 8RECh. 3 - Prob. 9RECh. 3 - Prob. 10RECh. 3 - Prob. 11RECh. 3 - Prob. 12RECh. 3 - Prob. 13RECh. 3 - Prob. 14RECh. 3 - Prob. 15RECh. 3 - Prob. 16RECh. 3 - Prob. 17RECh. 3 - Prob. 18RECh. 3 - Prob. 19RECh. 3 - Let S be the set of all real numbers in the...Ch. 3 - Prob. 21RE
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