Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences -- Instant Access (Pearson+)
14th Edition
ISBN: 9780137554805
Author: Raymond Barnett, Michael Ziegler
Publisher: PEARSON+
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Textbook Question
Chapter A.1, Problem 35E
Indicate true (T) or false (F), and for each false statement find real number replacements for a, b, and c that will provide a counterexample. For all real numbers a, b, and c,
(A) a(b – c) = ab – c
(B) (a – b) – c = a – (b – c)
(C) a(bc) = (ab)c
(D) (a ÷ b) ÷ c = a ÷ (b ÷ c)
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7. [10 marks]
Let G
=
(V,E) be a 3-connected graph. We prove that for every x, y, z Є V, there is a
cycle in G on which x, y, and z all lie.
(a) First prove that there are two internally disjoint xy-paths Po and P₁.
(b) If z is on either Po or P₁, then combining Po and P₁ produces a cycle on which
x, y, and z all lie. So assume that z is not on Po and not on P₁. Now prove that
there are three paths Qo, Q1, and Q2 such that:
⚫each Qi starts at z;
• each Qi ends at a vertex w; that is on Po or on P₁, where wo, w₁, and w₂ are
distinct;
the paths Qo, Q1, Q2 are disjoint from each other (except at the start vertex
2) and are disjoint from the paths Po and P₁ (except at the end vertices wo,
W1, and w₂).
(c) Use paths Po, P₁, Qo, Q1, and Q2 to prove that there is a cycle on which x, y, and
z all lie. (To do this, notice that two of the w; must be on the same Pj.)
Chapter A.1 Solutions
Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences -- Instant Access (Pearson+)
Ch. A.1 - State the real number property that justifies the...Ch. A.1 - Prob. 2MPCh. A.1 - You intend to give a 20% tip, rounded to the...Ch. A.1 - In Problems 16, replace each question mark with an...Ch. A.1 - Prob. 2ECh. A.1 - Prob. 3ECh. A.1 - In Problems 16, replace each question mark with an...Ch. A.1 - In Problems 16, replace each question mark with an...Ch. A.1 - In Problems 16, replace each question mark with an...Ch. A.1 - In Problems 726, indicate true (T) or false (F)....
Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - Prob. 14ECh. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - Prob. 21ECh. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - In Problems 726, indicate true (T) or false (F)....Ch. A.1 - Prob. 26ECh. A.1 - Prob. 27ECh. A.1 - If uv = 0, does either u or v have to be 0 ?...Ch. A.1 - Indicate whether the following are true (T) or...Ch. A.1 - Indicate whether the following are true (T) or...Ch. A.1 - Prob. 31ECh. A.1 - Give an example of a rational number that is not...Ch. A.1 - Given the sets of numbers N (natural numbers), Z...Ch. A.1 - Prob. 34ECh. A.1 - Indicate true (T) or false (F), and for each false...Ch. A.1 - Indicate true (T) or false (F), and for each false...Ch. A.1 - Prob. 37ECh. A.1 - Repeat Problem 37 for 0.181818 . 37.If c =...Ch. A.1 - Use a calculator to express each number in...Ch. A.1 - Prob. 40ECh. A.1 - In Problems 4144, without using a calculator,...Ch. A.1 - Prob. 42ECh. A.1 - Prob. 43ECh. A.1 - In Problems 4144, without using a calculator,...Ch. A.1 - Sales tax. Find the tax owed on a purchase of...Ch. A.1 - Sales tax. If you paid 29.86 in tax on a purchase...Ch. A.1 - Gasoline prices. If the price per gallon of gas...Ch. A.1 - Prob. 48E
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