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4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 2, Problem 55RE

Textbook Problem

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In Exercises *55* and 56, use the inclusion-exclusion formula to answer each application.

**55.** On a football team, 27 of its athletes play on offense, 22 play on defense, and 43 play on offense or defense. How many of the athletes play both on offense and on defense?

3

To determine

How many of the athletes play both on offense and on defense?

**Given information:**

On a football team, 27 of its athletes play on offense, 22 play on defense, and 43 play on offense or defense.

**Calculation:**

On a football team, 27 of its athletes play on offense, 22 play on defense, and 43 play on offense or defense.

Suppose O : athletes who play on offense. D : athletes who play on defense.

Therefore

The inclusion-exclusion formula is

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A college study categorized its seniors (S),...Ch. 2.4 - Given that set A has 47 elements and set B has 25...Ch. 2.4 - Given that set A has 16 elements, set B has 12...Ch. 2.4 - The following Venn diagram displaysU parceled into...Ch. 2.4 - Exactly one of the following equations is a valid...Ch. 2.5 - Use two disjoint sets to show that 0+2=0.Ch. 2.5 - Use two disjoint sets other than the set of even...Ch. 2.5 - Use sets toshow that 06=0.Ch. 2.5 - a. Use arrows to establish a one-to-one...Ch. 2.5 - Establish a one-to-one correspondence between the...Ch. 2.5 - Establish a one-to-one correspondence between D =...Ch. 2.5 - In Exercises 4 to 10, state the cardinality of...Ch. 2.5 - In Exercises 4 to 10, state the cardinality of...Ch. 2.5 - In Exercises 4 to 10, state the cardinality of...Ch. 2.5 - In Exercises 4 to 10, state the cardinality of...Ch. 2.5 - In Exercises 4 to 10, state the cardinality of...Ch. 2.5 - In Exercises 4 to 10, state the cardinality of...Ch. 2.5 - In Exercises 4 to 10, state the cardinality of...Ch. 2.5 - In Exercises 11 to 14, determine whether the given...Ch. 2.5 - In Exercises 11 to 14, determine whether the given...Ch. 2.5 - In Exercises 11 to 14, determine whether the given...Ch. 2.5 - In Exercises 11 to 14, determine whether the given...Ch. 2.5 - In Exercises 15 to 18, show that the given set is...Ch. 2.5 - In Exercises 15 to 18, show that the given set is...Ch. 2.5 - In Exercises 15 to 18, show that the given set is...Ch. 2.5 - In Exercises 15 to 18, show that the given set is...Ch. 2.5 - In Exercises 19 to 26, show that the given set has...Ch. 2.5 - In Exercises 19 to 26, show that the given set has...Ch. 2.5 - In Exercises 19 to 26, show that the given set has...Ch. 2.5 - In Exercises 19 to 26, show that the given set has...Ch. 2.5 - In Exercises 19 to 26, show that the given set has...Ch. 2.5 - In Exercises 19 to 26, show that the given set has...Ch. 2.5 - In Exercises 19 to 26, show that the given set has...Ch. 2.5 - In Exercises 19 to 26, show that the given set has...Ch. 2.5 - a. Place the set M = {3, 6,9, 12, 15, ...} of...Ch. 2.5 - Draw a figure that can be used to verify each of...Ch. 2.5 - Consider the semicircle with arc length it and...Ch. 2.5 - The Hubert Hotel is an imaginary hotel created by...Ch. 2 - In Exercises 1 to 6, use the roster method to...Ch. 2 - In Exercises 1 to 6, use the roster method to...Ch. 2 - In Exercises 1 to 6, use the roster method to...Ch. 2 - In Exercises 1 to 6, use the roster method to...Ch. 2 - In Exercises 1 to 6, use the roster method to...Ch. 2 - In Exercises 1 to 6, use the roster method to...Ch. 2 - In Exercises 7 to 10, use set-builder notation to...Ch. 2 - In Exercises 7 to 10, use set-builder notation to...Ch. 2 - In Exercises 7 to 10, use set-builder notation to...Ch. 2 - In Exercises 7 to 10, use set-builder notation to...Ch. 2 - In Exercises 11 and 12, state whether each of the...Ch. 2 - In Exercises 11 and 12, state whether each of the...Ch. 2 - In Exercises 13 to 16, determine whether the...Ch. 2 - In Exercises 13 to 16, determine whether the...Ch. 2 - In Exercises 13 to 16, determine whether the...Ch. 2 - In Exercises 13 to 16, determine whether the...Ch. 2 - In Exercises 17 to 24, let U = {2. 6, 8, 10, 12,...Ch. 2 - In Exercises 17 to 24, let U = {2. 6, 8, 10, 12,...Ch. 2 - In Exercises 17 to 24, let U = {2. 6, 8, 10, 12,...Ch. 2 - In Exercises 17 to 24, let U = {2. 6, 8, 10, 12,...Ch. 2 - In Exercises 17 to 24, let U = {2. 6, 8, 10, 12,...Ch. 2 - In Exercises 17 to 24, let U = {2. 6, 8, 10, 12,...Ch. 2 - In Exercises 17 to 24, let U = {2. 6, 8, 10, 12,...Ch. 2 - In Exercises 17 to 24, let U = {2. 6, 8, 10, 12,...Ch. 2 - In Exercises 25 and 26, determine whether the...Ch. 2 - In Exercises 25 and 26, determine whether the...Ch. 2 - In Exercises 27 to 30, determine whether the first...Ch. 2 - In Exercises 27 to 30, determine whether the first...Ch. 2 - In Exercises 27 to 30, determine whether the first...Ch. 2 - In Exercises 27 to 30, determine whether the first...Ch. 2 - In Exercises 31 to 34, list all the subsets of the...Ch. 2 - In Exercises 31 to 34, list all the subsets of the...Ch. 2 - In Exercises 31 to 34, list all the subsets of the...Ch. 2 - In Exercises 31 to 34, list all the subsets of the...Ch. 2 - In Exercises 35 to 38, find the number of subsets...Ch. 2 - In Exercises 35 to 38, find the number of subsets...Ch. 2 - In Exercises 35 to 38, find the number of subsets...Ch. 2 - In Exercises 35 to 38, find the number of subsets...Ch. 2 - In Exercises 39 and 40, determine whether each...Ch. 2 - In Exercises 39 and 40, determine whether each...Ch. 2 - In Exercises 41 to 44, draw a Venn diagram to...Ch. 2 - In Exercises 41 to 44, draw a Venn diagram to...Ch. 2 - In Exercises 41 to 44, draw a Venn diagram to...Ch. 2 - In Exercises 41 to 44, draw a Venn diagram to...Ch. 2 - In Exercises 45 to 48, draw Venn diagrams to...Ch. 2 - In Exercises 45 to 48, draw Venn diagrams to...Ch. 2 - In Exercises 45 to 48, draw Venn diagrams to...Ch. 2 - In Exercises 45 to 48, draw Venn diagrams to...Ch. 2 - In Exercises 49 and 50, use set notation to...Ch. 2 - In Exercises 49 and 50, use set notation to...Ch. 2 - In Exercises 51 and 52, draw a Venn diagram with...Ch. 2 - In Exercises 51 and 52, draw a Venn diagram with...Ch. 2 - In a survey at a health club, 208 members...Ch. 2 - A gourmet coffee bar conducted a survey to...Ch. 2 - In Exercises 55 and 56, use the...Ch. 2 - In Exercises 55 and 56, use the...Ch. 2 - In Exercises 57 to 60, establish a one-to-one...Ch. 2 - In Exercises 57 to 60, establish a one-to-one...Ch. 2 - In Exercises 57 to 60, establish a one-to-one...Ch. 2 - In Exercises 57 to 60, establish a one-to-one...Ch. 2 - In Exercises 61 and 62, show that the given set is...Ch. 2 - In Exercises 61 and 62, show that the given set is...Ch. 2 - In Exercises 63 to 70, state the cardinality of...Ch. 2 - In Exercises 63 to 70, state the cardinality of...Ch. 2 - In Exercises 63 to 70, state the cardinality of...Ch. 2 - In Exercises 63 to 70, state the cardinality of...Ch. 2 - In Exercises 63 to 70, state the cardinality of...Ch. 2 - In Exercises 63 to 70, state the cardinality of...Ch. 2 - In Exercises 63 to 70, state the cardinality of...Ch. 2 - In Exercises 63 to 70, state the cardinality of...Ch. 2 - In Exercises 71 and 72, find each of the...Ch. 2 - In Exercises 71 and 72, find each of the...Ch. 2 - In Exerciseslto4,letUâ€”{1,2,3,4,5,6,7,8,9, 10), A...Ch. 2 - In Exerciseslto4,letU={1,2,3,4,5,6,7,8,9, 10}, A =...Ch. 2 - In Exercises 1 to 4, let U = {1, 2, 3, 4, 5, 6, 7,...Ch. 2 - In Exercises 1 to 4, let U = {1, 2, 3, 4, 5, 6, 7,...Ch. 2 - In Exercises 5 and 6, use set-builder notation to...Ch. 2 - In Exercises 5 and 6, use set-builder notation to...Ch. 2 - State the cardinality of each set. a. The set of...Ch. 2 - In Exercises 8 and 9, state whether the given sets...Ch. 2 - In Exercises 8 and 9, state whether the given sets...Ch. 2 - List all of the subsets of {a, b, c, d}.Ch. 2 - Determine the number of subsets of a set with 21...Ch. 2 - In Exercises 12 and 13, draw a Venn diagram to...Ch. 2 - In Exercises 12 and 13, draw a Venn diagram to...Ch. 2 - Use one of Dc Morgans laws to write (A âˆª B) as...Ch. 2 - Upgrade Options An automobile company makes a...Ch. 2 - Student Demographics A college finds that 841 of...Ch. 2 - The following bar graph shows the monthly...Ch. 2 - A survey of 1000 households was taken to determine...Ch. 2 - Show a method that can be used to establish a...Ch. 2 - Verify that the following set is an infinite set...

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