Explanation Given information: N ( A ∩ B ) = N ( U ) − N ( ( A ∩ B ) c ) Concept used: Difference rule Calculation: A and B Are sets in a finite universe U To determine (b) The rule applied in N ( A ∩ B ) = N ( U ) − N ( ( A ∪ B ) c ) . To determine (c) The property applied for the step N ( A ∩ B ) = N ( U ) − ( N ( A c ) + N ( B c ) − N ( A C ∩ B C ) ) .

5th Edition

ISBN: 9781337694193

Author: EPP, Susanna S.

Publisher: Cengage Learning,

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Chapter 9.3, Problem 36ES

To determine

(a)

The rule applied in N(A∩B)=N(U)−N(( A∩B)c).

To determine

(b)

The rule applied in N(A∩B)=N(U)−N(( A∪B)c).

To determine

(c)

The property applied for the step N(A∩B)=N(U)−(N(Ac)+N(Bc)−N(AC∩BC)).

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Chapter 9.3, Problem 35ES

Chapter 9.3, Problem 37ES

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Chapter 9 Solutions

Discrete Mathematics With Applications

Ch. 9.1 - A sample space of a random process or experiment...Ch. 9.1 - An event in a sample space is .Ch. 9.1 - To compute the probability of an event using the...Ch. 9.1 - Prob. 4TY Ch. 9.1 - Toss two coins 30 times and make a table showing...Ch. 9.1 - In the example of tossing two quarters, what is...Ch. 9.1 - In 3-6 use the sample space given in Example...Ch. 9.1 - In 3-6 use the sample space given in Example...Ch. 9.1 - In 3-6 use the sample space given in Example...Ch. 9.1 - In 3-6 use the sample space given in Example...

Ch. 9.1 - In 7-10, use the sample space given in Example...Ch. 9.1 - In 7-10, use the sample space given in Example...Ch. 9.1 - In 7-10, use the sample space given in Example...Ch. 9.1 - In 7-10, use the sample space given in Example...Ch. 9.1 - Suppose that a coin is tossed three times and the...Ch. 9.1 - Suppose that each child born is equally likely to...Ch. 9.1 - Suppose that on a true/false exam you have no idea...Ch. 9.1 - There people have been exposed to a certain...Ch. 9.1 - Prob. 15ES Ch. 9.1 - Two faces of a six-sided die are painted red, two...Ch. 9.1 - Prob. 17ES Ch. 9.1 - Prob. 18ES Ch. 9.1 - An urn contains two blue balls (denoted B1 and B2)...Ch. 9.1 - Relet to Example 9.1.3. Suppose you are appealing...Ch. 9.1 - Prob. 21ES Ch. 9.1 - a. How many positive three-digit integers are...Ch. 9.1 - Suppose A[1],A[2],A[3],....,A[n] is a...Ch. 9.1 - Suppose A[1],A[2],...,A[n] is a one-dimensional...Ch. 9.1 - Suppose A[1], A[2],…A[n] is a one-dimensional...Ch. 9.1 - Prob. 26ES Ch. 9.1 - What is the 62nd element in the one-dimensional...Ch. 9.1 - If the largest of 56 consecutive integers is 279,...Ch. 9.1 - Prob. 29ES Ch. 9.1 - How many even integers are between 1 and 1,.001?Ch. 9.1 - Prob. 31ES Ch. 9.1 - A certain non-leap year has 365 days, and January...Ch. 9.1 - Prove Theorem 9.1.1. (Let m be any integer and...Ch. 9.2 - The multiplication rule says that if an operation...Ch. 9.2 - A permutation of a set of elements is_________.Ch. 9.2 - Prob. 3TY Ch. 9.2 - Prob. 4TY Ch. 9.2 - Prob. 5TY Ch. 9.2 - Prob. 6TY Ch. 9.2 - Prob. 1ES Ch. 9.2 - Prob. 2ES Ch. 9.2 - Prob. 3ES Ch. 9.2 - Prob. 4ES Ch. 9.2 - Prob. 5ES Ch. 9.2 - One urn contains two black balls (Labeled B1 and...Ch. 9.2 - One urn contains one blue ball (labeled B1) and...Ch. 9.2 - A person buying a personal computer system is...Ch. 9.2 - Suppose there are three roads from city A to city...Ch. 9.2 - Suppose there are three routes from North Point to...Ch. 9.2 - (a)A bit string is a finite sequence of 0’s and...Ch. 9.2 - Hexadecimal numbers are made using the sixteen...Ch. 9.2 - A coin is tossed four times. Each time the result...Ch. 9.2 - Suppose that in a certain stale, all automobile...Ch. 9.2 - A combination lock requires three selections of...Ch. 9.2 - a. 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P(n+1,3)=n3n Ch. 9.2 - Prob. 41ES Ch. 9.2 - Prob. 42ES Ch. 9.2 - Prob. 43ES Ch. 9.2 - Prove Theorem 9.2.1 by mathematical induction.Ch. 9.2 - Prove Theorem 9.2.2 by mathematical induction.Ch. 9.2 - Prob. 46ES Ch. 9.2 - Prob. 47ES Ch. 9.3 - The addition rule says that if a finite set A...Ch. 9.3 - Prob. 2TY Ch. 9.3 - Prob. 3TY Ch. 9.3 - Prob. 4TY Ch. 9.3 - Prob. 5TY Ch. 9.3 - (a) How many bit string consist of from one...Ch. 9.3 - (a) How many string of hexadecimal digits consist...Ch. 9.3 - (a) How many integers from 1 through 999 do not...Ch. 9.3 - How many arrangements in a row of no more than...Ch. 9.3 - (a) How many five-digit integers (integers from...Ch. 9.3 - In a certain stale, all license plain consist of...Ch. 9.3 - At a certain company, passwords must be from...Ch. 9.3 - In a certain country license plates consist of...Ch. 9.3 - a. Consider the following algorithm segment: for...Ch. 9.3 - A calculator has an eight-digit display and a...Ch. 9.3 - a. 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A store sells 8 colors of balloons with at...Ch. 9.6 - A large pile of coins consists of penruey nickels,...Ch. 9.6 - Suppose the bakery in exercise 3 has at least...Ch. 9.6 - Suppose the camera shop in exercise 4 can obtain...Ch. 9.6 - Prob. 21ES Ch. 9.7 - If n and r are nonnegative integers with rn , then...Ch. 9.7 - Prob. 2TY Ch. 9.7 - Prob. 3TY Ch. 9.7 - Prob. 4TY Ch. 9.7 - Prob. 5TY Ch. 9.7 - Prob. 6TY Ch. 9.7 - Prob. 7TY Ch. 9.7 - Prob. 1ES Ch. 9.7 - Prob. 2ES Ch. 9.7 - Prob. 3ES Ch. 9.7 - Prob. 4ES Ch. 9.7 - Prob. 5ES Ch. 9.7 - Prob. 6ES Ch. 9.7 - Prob. 7ES Ch. 9.7 - Prob. 8ES Ch. 9.7 - Prob. 9ES Ch. 9.7 - (a) Use Pascal’s triangle given in Table 9.7.1 to...Ch. 9.7 - Prob. 11ES Ch. 9.7 - Use Pascal’s formula repeatedly to derive a...Ch. 9.7 - Use Pascal’s formula to prove by mathematical...Ch. 9.7 - Prob. 14ES Ch. 9.7 - Prove the following generalization of exercise 13:...Ch. 9.7 - Prob. 16ES Ch. 9.7 - Prove that for every integer n0 ,...Ch. 9.7 - Prob. 18ES Ch. 9.7 - Prob. 19ES Ch. 9.7 - Prob. 20ES Ch. 9.7 - Prob. 21ES Ch. 9.7 - Use the binomial theorem to expand the expressions...Ch. 9.7 - Use the binomial theorem to expand the expressions...Ch. 9.7 - Use the binomial theorem to expand the expressions...Ch. 9.7 - Prob. 25ES Ch. 9.7 - Prob. 26ES Ch. 9.7 - Prob. 27ES Ch. 9.7 - Prob. 28ES Ch. 9.7 - Prob. 29ES Ch. 9.7 - Prob. 30ES Ch. 9.7 - In 29-34, find the coefficient of the given term...Ch. 9.7 - In 29-34, find the coefficient of the given term...Ch. 9.7 - Prob. 33ES Ch. 9.7 - In 29-34, find the coefficient of the given term...Ch. 9.7 - Prob. 35ES Ch. 9.7 - For every integer n1 ,...Ch. 9.7 - Prob. 37ES Ch. 9.7 - Prob. 38ES Ch. 9.7 - Prob. 39ES Ch. 9.7 - Prob. 40ES Ch. 9.7 - Prob. 41ES Ch. 9.7 - Prob. 42ES Ch. 9.7 - Prob. 43ES Ch. 9.7 - Prob. 44ES Ch. 9.7 - Prob. 45ES Ch. 9.7 - Prob. 46ES Ch. 9.7 - Prob. 47ES Ch. 9.7 - Prob. 48ES Ch. 9.7 - Prob. 49ES Ch. 9.7 - Prob. 50ES Ch. 9.7 - Express each of the sums in 43—54 in closed form...Ch. 9.7 - Prob. 52ES Ch. 9.7 - Prob. 53ES Ch. 9.7 - Prob. 54ES Ch. 9.7 - Prob. 55ES Ch. 9.8 - If A is an event in a sample space S,P(A) can...Ch. 9.8 - Prob. 2TY Ch. 9.8 - Prob. 3TY Ch. 9.8 - Prob. 4TY Ch. 9.8 - Prob. 5TY Ch. 9.8 - Prob. 1ES Ch. 9.8 - Prob. 2ES Ch. 9.8 - Prob. 3ES Ch. 9.8 - Prob. 4ES Ch. 9.8 - Prob. 5ES Ch. 9.8 - Prob. 6ES Ch. 9.8 - Prob. 7ES Ch. 9.8 - Prob. 8ES Ch. 9.8 - Let A and B be events in a sample space S, and let...Ch. 9.8 - Prob. 10ES Ch. 9.8 - Prob. 11ES Ch. 9.8 - Prob. 12ES Ch. 9.8 - Prob. 13ES Ch. 9.8 - A lottery game offers $2 million to the grand...Ch. 9.8 - A company offers a raffle whose grand prize is a...Ch. 9.8 - An urn contains four balls numbered 2, 2, 5, and...Ch. 9.8 - Prob. 17ES Ch. 9.8 - An urn contains five balls numbered 1,2,2,8, and...Ch. 9.8 - Prob. 19ES Ch. 9.8 - Suppose a person offers to play a game with you....Ch. 9.8 - Prob. 21ES Ch. 9.8 - Prob. 22ES Ch. 9.8 - Prob. 23ES Ch. 9.9 - Prob. 1TY Ch. 9.9 - Prob. 2TY Ch. 9.9 - Prob. 3TY Ch. 9.9 - Prob. 4TY Ch. 9.9 - Prob. 1ES Ch. 9.9 - Prob. 2ES Ch. 9.9 - Prob. 3ES Ch. 9.9 - Prob. 4ES Ch. 9.9 - Suppose that A and B are events in a sample space...Ch. 9.9 - An urn contains 25 red balls and 15 blue balls....Ch. 9.9 - Prob. 7ES Ch. 9.9 - A pool of 10 semifinalists for a job consists of 7...Ch. 9.9 - Prob. 9ES Ch. 9.9 - Prob. 10ES Ch. 9.9 - One urn contains 12 blue balls and 7 white balls,...Ch. 9.9 - Redo exercise 11 assuming that the first urn...Ch. 9.9 - Prob. 13ES Ch. 9.9 - Prob. 14ES Ch. 9.9 - Prob. 15ES Ch. 9.9 - Three different supplier.-X, Y. and Z-provide...Ch. 9.9 - Prob. 17ES Ch. 9.9 - Prob. 18ES Ch. 9.9 - Prob. 19ES Ch. 9.9 - Prob. 20ES Ch. 9.9 - Prob. 21ES Ch. 9.9 - Prob. 22ES Ch. 9.9 - Prob. 23ES Ch. 9.9 - Prob. 24ES Ch. 9.9 - A coin is loaded so that the probability of heads...Ch. 9.9 - Describe a sample space and events A,B, and C,...Ch. 9.9 - Prob. 27ES Ch. 9.9 - Prob. 28ES Ch. 9.9 - Suppose that ten items are chosen at random from a...Ch. 9.9 - Suppose the probability of a false positive result...Ch. 9.9 - Prob. 31ES Ch. 9.9 - Prob. 32ES Ch. 9.9 - Prob. 33ES Ch. 9.9 - Prob. 34ES

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