Exam 8: Sets and Logic

A survey of 650 members of a club asked the following questions: For each statement, if your answer is yes, check the box. , I watched a movie at a theater in the past month. , I watched a rented movie at home in the past month. If 135 respondents checked the first box, what percent of the respondents watched a movie at a theater in the past month? __________% went to a theater If 305 respondents checked the second box, what percent of the respondents watched a rented movie at home in the past month? __________% watched a movie at home If 60 checked both boxes, what percent of the respondents watched movies both in a theater and at home? __________% watched a movies at home and in a theater What percent of the members watched a movie in a theater or at home in the past month? __________% watched a movie at home or in a theater Round your answers to the nearest tenth of a percent.

Construct a truth table for the statement. cellpadding ="0" cellspacing ="0" width ="96\%" border ="1">

Which conclusion is valid? All Turtles have shells. Yertle is a Turtle.

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {1, 4, 6, 8} B = {4, 3, 5, 7} C = {4, 6, 8} List all the members of the set. $\varnothing$

Specify the set by roster. {U.S. president in 2010}

In a recent survey of $100$ women, the following information was gathered: $56$ use shampoo A. $51$ use shampoo B. $35$ use shampoo C. $23$ use shampoos A and B. $19$ use shampoos A and C. $14$ use shampoos B and C. $12$ use all three. How many are using all three shampoos (Region VII)? A = {women who use shampoo A } B = {women who use shampoo B } C = {women who use shampoo C } Use the figure (with Regions I to VIII) to answer the question.

A poll was taken of $100$ students at a commuter campus to find out how they got to campus. The results were: $44$ said they drove alone. $33$ rode the bus. $28$ rode in a carpool. $7$ used both carpools and rode the bus. $10$ used both a carpool and sometimes drove alone. $5$ used buses as well as drove alone. $3$ used all three methods. How many are C only (Region III)? A = {people who drive alone} B = {people who ride the bus} C = {people who carpool} Use the figure (with Regions I to VIII) to answer the question. __________ students

Write the words in symbols: The set G is a subset of itself.

Give the numbers of elements in the region marked VIII in the figure. $| U | = 2,200 , | A | = 156 , | B | = 813 , | C | = 283 , | A \cap B | = 88$ $| A \cap C | = 91 , | B \cap C | = 60 , | A \cap B \cap C | = 37$

Use Venn diagrams to check the validity of the argument. All palms are trees. The plant is not a tree. Therefore, the plant is not a palm.

Let U=\{1,2,3,4,5,6,7,8,9,10\} A=\{3,5,7\} B=\{5,8,9\} List all the members of the set. $A \cup B$

Bookdale Community College enrolled 15,000 students in the fall of 2011. It was reported that of that number, 54% were female and 46%% were male. In addition, 61% were under the age of 21. How many students were there in each category: females, males, and under 21?

Write in words what the symbols $C \subset D$ mean about sets C and D.

Specify the set by roster. {even counting numbers less than 12}

List all subsets of the given set. Identify any of the subsets that are improper. $\{ z , n , l , r \}$

In a sample of defective tires, 72 have defects in materials, 99 have defects in workmanship, and 17 have defects of both types. How many tires are in the sample?

Tell whether you believe the conjecture is true or false. The product of two odd numbers is odd.

Let U=\{1,2,3,4,5,6,7,8,9,10\} A=\{1,2,4,5,6\} B=\{1,2,3,5,6\} List all the members of the set. $\bar { A }$

Let U=\{1,2,3,4,5,6,7,8,9,10\} A=\{2,3,4,5,6\} B=\{6,7,8,9,10\} List all the members of the set. $A \cap B$

Use set notation to identify the shaded portion of the Venn diagram.