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Test Bank For Math in Our World, 4th Edition

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    MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Determine whether the type of reasoning used is inductive or deductive reasoning. If a computer tech says it will cost $225 to fix my computer , it will actually cost $300 . Since a computer tech told me it would cost $225 to fix my computer , I can expect it to cost me $300 . A) deductive reasoning B) inductive reasoning Answer: A 2) Determine whether the type of reasoning used is inductive or deductive reasoning. Victor has already lost 3 cameras . He didn't spend a lot of money on his newest camera because he knows he'll eventually lose that one too. A) inductive reasoning B) deductive reasoning Answer: A SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 3) Use inductive reasoning to find a pattern, and then make a reasonable conjecture for the next number in the sequence. 7 8 10 13 17 22 28 Answer: 35 4) Use inductive reasoning to find a pattern, and then make a reasonable conjecture for the next number in the sequence. 1 4 16 64 256 Answer: 1,024 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 5) Use inductive reasoning to find a pattern, and then make a reasonable conjecture for the next number in the sequence. 20 25 22 27 24 29 26 31 A) 34 B) 36 C) 26 D) 28 Answer: D 6) Use inductive reasoning to find a pattern, and then make a reasonable conjecture for the next number in the sequence. 1 3 7 13 15 19 25 27 31 37 A) 39 B) 45 C) 41 D) 43 Answer: A 1

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    7) Use inductive reasoning to find a pattern for the answers. Then use the pattern to guess the result of the final calculation, and perform the operation to see if your answer is correct. 0 2 + 1 = 1 1 2 + 3 = 2 2 2 2 + 5 = 3 2 3 2 + 7 = 4 2 4 2 + 9 = 5 2 . . . 10 2 + 21 = ? A) 111 B) 12 2 C) 11 2 D) 120 Answer: C 8) Use inductive reasoning to find a pattern for the answers. Then use the pattern to guess the result of the final calculation, and perform the operation to see if your answer is correct. 12,345,679 × 9 = 111,111,111 12,345,679 × 18 = 222,222,222 12,345,679 × 27 = 333,333,333 . . . 12,345,679 × 45 = ? A) 555,555,510 B) 444,444,444 C) 666,666,666 D) 555,555,555 Answer: D 9) Write a counter example to show that the statement is false. When an odd number is added to the product of two even numbers, the result will be even. A) 4 Â 5 + 2 = 22. 22 is even. B) 3 Â 5 + 4 = 19. 19 is not even. C) 4 Â 2 + 3 = 11. 11 is not even. D) 4 Â 5 + 1 = 21. 21 is not even. Answer: C 10) Write a counter example to show that the statement is false. When any number is multiplied by 5 and the digits of the answer are added, the sum will be divisible by 5 . A) 111 × 5 = 555 ; 5 + 5 + 5 = 15 , which is not divisible by 5 . B) 11 × 5 = 55 ; 5 + 5 = 10 , which is divisible by 5 . C) 2 × 5 = 10 ; 1 + 0 = 1 , which is not divisible by 5 . D) 10 × 5 = 50 ; 5 + 0 = 5 , which is divisible by 5 . Answer: C 2

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    ESSAY. Write your answer in the space provided or on a separate sheet of paper. 11) Read the following scenario and determine whether the type of reasoning used by Leanne is inductive or deductive. Explain how you decided. Leanne was concerned that if she continued to be late for work, she would lose her job. Answer: Deductive. Leanne knew that consistently being late can cause one to lose their job, so she reasoned that her tardiness could cause this to happen. 12) Read the following scenario and determine whether the type of reasoning used by Paul is inductive or deductive. Explain how you decided. Paul knew that his friend, Leanne, had been late the past 8 workdays, so he didn't save a seat for her at morning meeting. Answer: Inductive. Paul assumed that because Leanne had a pattern of being late, this pattern would continue. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 13) Use inductive reasoning to conjecture the rule that relates the number you selected to the final answer. Try to prove your conjecture using deductive reasoning. Select a number: Multiply by 7 : Subtract 56 from the answer: Divide by 7 : Subtract the original number: Answer: Final answer is always -8 . Select a number: x Multiply by 7 : 7 x Subtract 56 from the answer: 7 x - 56 Divide by 7 : 7 x - 56 7 = x - 8 Subtract the original number: x - 8 - x = -8 3

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    MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 14) Use inductive reasoning to make a conjecture about a rule that relates the original number to the final answer. Try to prove your conjecture using deductive reasoning. Select a number. Add 90 . Multiply by 6 . Subtract 540 . Divide by 6 . Subtract the original number. A) The answer is always the original number. B) The answer is always 450 . C) The answer is always -450 . D) The answer is always 0. Answer: D 15) Use deductive reasoning to arrive at a conclusion. On Christmas Day, Japanese restaurants and ski slopes are always open, so this Christmas Day we can A) eat Japanese food and go skiing . B) watch football and open gifts. C) eat Mexican food and go skiing . D) eat fast food and go skiing . Answer: A SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 16) Round to the nearest ten . 202 Answer: 200 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 17) Round to the nearest hundredth. 2.87491 A) 2.87500 B) 2.88000 C) 2.87400 D) 2.87000 Answer: D 18) Round 560,565,131 to the nearest ten-million . A) 560,000,000 B) 560,570,000 C) 561,000,000 D) 600,000,000 Answer: A SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 19) An item that originally cost $279.99 is on sale for 20 % off. Estimate the sale price of the item. Answer: $224 - $240 4

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    20) Estimate the total cost of the following meal at a sub shop. sandwich $4.89 chips $1.24 soda $0.99 Answer: approximately $7 21) Bob and Sue are celebrating their 5th wedding anniversary. Estimate the total cost of their evening based on the prices below: theater $63 . 59 dinner $76 . 83 drinks $17 . 71 taxi $13 . 25 Answer: approximately $172 22) Estimate the cost to live in an apartment for 1 year if the rent is $209 per month and utilities are $64 per month. Answer: approximately $3,240 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 23) For a specific year, the average household income for selected states is shown here. Estimate the difference between the highest and lowest average incomes. A) $32,000 B) $15,000 C) $40,000 D) $23,000 Answer: D 5

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    SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 24) For a specific year, the average household income for selected states is shown here. Estimate the average household income for Ohio . Answer: $43,000 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 25) The demographics of an elementary school are shown below. The school has 291 students. Estimate the number of students who are White Non-Hispanic . A) 9,603 B) 33 C) 10 D) 96 Answer: D 6

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    26) Estimate the number of people living in the US in 1,900 . A) 76,000,000 B) 96,000,000 C) 56,000,000 D) 9,600,000 Answer: A 27) The manager of an Internet cafe is having new counters custom-made . She wants to put 8 PCs on each counter with 3 feet between the PCs and 2 feet on each end. The PCs measure 18 inches wide and 24 inches high. What length of counters should the Internet cafe have made? A) 40 ft B) 37 ft C) 38 ft D) 41 ft Answer: B 28) The length of a garden is double its width. There is a fence around the perimeter that measures 114 ft . What are the length and width of the garden? A) length = 38 ft, width = 19 ft B) length = 28.5 ft, width = 57 ft C) length = 57 ft, width = 28.5 ft D) length = 19 ft, width = 38 ft Answer: A SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 29) One number is 21 more than another number. The sum of the numbers is 29 . Find the numbers. Answer: 4 and 25 30) Arrange the digits 3 , 4 , and 9 to form two numbers divisible by 6. Answer: 394 and 934 7

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    MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 31) Phil has 12 stamps of denominations $0.37 and $0.23 . If the total value of the stamps is $4.02 how many $0.37 stamps does Phil have? A) 3 B) 10 C) 8 D) 9 Answer: D SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 32) The peak rate of a phone company is 22 ¢ per minute, and the off-peak rate is 12 ¢ per minute. Find the savings for a 23 -minute phone call if it was made during off-peak time as opposed to peak time. Answer: $2.30 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 33) Jane has 15 phone cards worth either $20 or $15 . How many of each does he have if the phone cards total $245 ? A) three $20 cards and twelve $15 cards B) eleven $20 cards and four $15 cards C) four $20 cards and eleven $15 cards D) seven $20 cards and seven $15 cards Answer: C 34) A person's monthly budget includes $236 for food, $165 for gasoline, and $170 for utilities. If the person earns $2,406 per month, how much money is left for other expenses? A) $2,005 B) $918 C) $1,835 D) $2,071 Answer: C 35) A recipe calls for 3 cups of flour. If the baker wants to make half a recipe, how much flour should be used? A) 2 3 cup B) 6 cups C) 5 cups D) 1 1 2 cups Answer: D 36) A car travels 348 miles on 5.6 gallons of gasoline. How many miles per gallon did the car get? (Round to the nearest tenth.) A) 56.6 miles per gallon B) 64.5 miles per gallon C) 16.1 miles per gallon D) 62.1 miles per gallon Answer: D 8

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    MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) State whether the collection is well-defined or not well-defined . {5, . . . } A) Well-defined B) Not well-defined Answer: B 2) Let ǹ = {6, 7, 8, 9, 10}. State whether the following statement true or false: 8 ' ǹ A) True B) False Answer: B 3) Write the set using roster notation: The set of even natural numbers less than 10. A) { x x % ȃ and x < 10} B) { x x % Ǽ and x < 10} C) {2, 4, 6, 8, 10} D) {2, 4, 6, 8} Answer: D 4) Write the set using roster notation: { x x % ȃ and x > 24 } A) { 25 , 26 , 27 , 28 , . . .} B) { x x is a natural number less than 24 } C) { x x is a natural number greater than 24 } D) { 24 , 25 , 26 , 27 , . . .} Answer: A 5) Write the set using the descriptive method: { 9 , 18 , 27 , 36 , 45 } A) { x x is a natural number between 9 and 45 } B) The set natural numbers between 9 and 45 . C) { x x is a multiple of 9 less than 46 } D) The set of the first five positive multiples of 9 . Answer: D SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 6) Write the set using the descriptive method: { 25 , 26 , 27 , . . . , 45 } Answer: The set of natural numbers from 25 to 45 , inclusive. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 7) Write the set using set-builder notation: The set of natural numbers greater than 11. A) {12, 13, 14, 15, . . .} B) { x x % ȃ and x > 11} C) {11, 12, 13, 14, . . .} D) { x x > 11} Answer: B 1

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    8) Write the set using set-builder notation: {1, 3, 5, . . . , 27 } A) { x x % ȃ and x < 28 } B) { x x % ȅ and x < 27 } C) { x x is an odd natural number less than 27 } D) { x x is an odd natural number less than 28 } Answer: D SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 9) List the elements in the set: { 7 , 10 , 13 , . . . , 31 }. Answer: { 7 , 10 , 13 , 16 , 19 , 22 , 25 , 28 , 31 } MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 10) The graph below displays the median housing prices for all houses sold in Anywhere, US between 2003 and 2008. Median Home Prices in Anywhere List the set of years in which the median price was above $150,000 . A) (2005, 2006, 2007, 2008} B) (2003, 2004} C) (2005, 2006, 2007} D) (2003, 2004, 2008} Answer: C 11) Which statement is true? A) { 9 , 3 , 0 }  { 3 , 0 , 9 } B) n ( + ) = 0 C) +  ^ + ` D) All equivalent sets are equal. Answer: B 2

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    12) State whether the following set is empty. { x | x is a natural number divisible by 7} A) Yes B) No Answer: B 13) Find the cardinal number for the set. ǹ = { 3 , 6 , 9 , . . . , 33 } A) The set is infinite. B) n ( ǹ ) = 33 C) n ( ǹ ) = 11 D) n ( ǹ ) = 4 Answer: C 14) Find the cardinal number for the set. Ǻ = { eight } A) n ( Ǻ ) = 8 B) n ( Ǻ ) = 5 C) n ( Ǻ ) = 0 D) n ( Ǻ ) = 1 Answer: D 15) Which set is finite? A) { x x % ȃ and x is odd} B) {2, 4, 6, 8, 10, 12, . . .} C) { x x % ȃ and x > 100} D) { x x % ȃ and x < 100} Answer: D 16) Which set is infinite? A) { x x is an improper fraction} B) { x x % ȃ and x < 20} C) + D) {3, 5, 7, . . ., 99} Answer: A 17) Classify each pair of sets as equal, equivalent, or neither. {a, b, c, d, e} and {5, 4, 3, 2, 1} A) equivalent B) neither C) equal and equivalent Answer: A 18) Classify each pair of sets as equal, equivalent, or neither. {1, 3, 5} and {2, 4, 6, 8} A) neither B) equivalent C) equal and equivalent Answer: A 19) Classify each pair of sets as equal, equivalent, or neither. {1, 2, 3, . . ., 10} and {10, 9, 8, . . ., 1} A) equal and equivalent B) neither C) equivalent Answer: A 3

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    20) Show that the pair of sets is equivalent by using a one-to-one correspondence. { x x is an odd natural number between 8 and 20 } and { x x is an even natural number between 13 and 25 } A) { 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 } Ľ Ľ Ľ Ľ Ľ Ľ Ľ Ľ Ľ Ľ Ľ { 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 } B) { 9 , 11 , 13 , 15 , 17 , 19 } Ľ Ľ Ľ Ľ Ľ Ľ { 14 , 16 , 18 , 20 , 22 , 24 } C) { 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 } Ľ Ľ Ľ Ľ Ľ Ľ Ľ Ľ Ľ Ľ Ľ Ľ Ľ { 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 } D) { 8 , 10 , 12 , 14 , 16 , 18 , 20 } Ľ Ľ Ľ Ľ Ľ Ľ Ľ { 13 , 15 , 17 , 19 , 20 , 22 , 23 } Answer: B 21) Let U = { 8 , 16 , 24 , 32 , 40 , 48 , 56 , 64 } and A = { 24 , 32 , 40 , 56 }. A' A) A' = { 8 , 16 , 64 } B) A' = + C) A' = { 8 , 16 , 48 , 64 } D) A' = {0} Answer: C 22) ƍ Use the Venn diagram and find B . A) ƍ B = { p, q, r, s, t } B) ƍ B = { p, q, r, s, t, w, x } C) ƍ B = { p, q, r, w, x } D) ƍ B = { p, q, r } Answer: C 4

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    23) Let U = {5, 10, 15, 20, 25, 30, 35, 40} A = {5, 10, 15, 20} B = {25, 30, 35, 40} C = {10, 20, 30, 40}. Find C' . A) C' = {5, 15, 25, 35} B) C' = {5, 10, 15, 20, 25, 30, 35, 40} C) C' = {10, 20, 30, 40} D) C' = + Answer: A SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 24) Find all subsets of the set. { 2 , 4 , 9 }. Answer: + ; { 2 }; { 4 }; { 9 }; { 2 , 4 }; { 2 , 9 }; { 4 , 9 }; { 2 , 4 , 9 } MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 25) Find all proper subsets of the set. { c , f , x } A) + ; { c }; { f }; { x }; { c , f }; { c , x }; { f , x } B) + ; { c , f }; { c , x }; { f , x }; { c , f , x } C) + ; { c , f }; { c , x }; { f , x } D) + ; { c }; { f }; { x }; { c , f }; { c , x }; { f , x }; { c , f , x } Answer: A 26) True or False? {4} 5 {2, 4, 6, 8, 10} A) False B) True Answer: B 27) True or False? {4} % {2, 4, 6, 8, 10, . . . } A) False B) True Answer: A 28) Which statement is false? A) + 5 {a, b, c} B) + 2 {a, b, c} C) a % {a, b, c} D) + % {a, b, c} Answer: D 29) Find the number of subsets the set has. { 1, 2, 3, 4, 5 } A) 16 B) 31 C) 5 D) 32 Answer: D 30) Find the number of proper subsets the set has. { m, n, p } A) 8 B) 3 C) 7 D) 6 Answer: C 5

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    31) Since the student union is being remodeled, there is a limited choice of foods and drinks a student can buy for a snack between classes. Students can choose none, some, or all of these items: diet soft drink, cheeseburger, fries . How many different selections can be made? A) 9 B) 3 C) 7 D) 8 Answer: D 32) Use the Venn diagram and find A ŀ Ǻ . A) A ŀ B = { q, r, s, v, w } B) A ŀ B = { q, r, s, v, w, x, y } C) A ŀ B = { q, r, s, t, u, v, w } D) A ŀ B = { t, u } Answer: D 33) Let U = {5, 10, 15, 20, 25, 30, 35, 40} A = {5, 10, 15, 20} V = {25, 30, 35, 40} C = {10, 20, 30, 40}. Find A 1 C . A) A 1 C = {5, 10, 15, 20, 30, 40} B) A 1 C = + C) A 1 C = {10, 20} D) A 1 C = {5, 15, 30, 40} Answer: A 34) Let U = {5, 10, 15, 20, 25, 30, 35, 40} A = {5, 10, 15, 20} B = {25, 30, 35, 40} C = {10, 20, 30, 40}. Find A ŀ B . A) A ŀ B = {10, 15} B) A ŀ B = {5, 10, 35, 40} C) A ŀ B = {5, 10, 15, 20, 25, 30, 35, 40} D) A ŀ B = + Answer: D 6

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    35) ƍ Let U = {5, 10, 15, 20, 25, 30, 35, 40} A = {5, 10, 15, 20} B = {25, 30, 35, 40} C = {10, 20, 30, 40}. Find A' ŀ ( B 1 C' ). A) A' ŀ ( B' 1 C' ) = 5, 10, 15, 20, 25, 30, 35, 40} B) A' ŀ ( B' 1 C' ) = + C) A' ŀ ( B' 1 C' ) = {10, 20, 25, 30, 35, 40} D) A' ŀ ( B' 1 C' ) = {25, 35} Answer: D 36) Let U = {5, 10, 15, 20, 25, 30, 35, 40} A = {5, 10, 15, 20} B = {25, 30, 35, 40} C = {10, 20, 30, 40}. Find B ŀ C' . A) B ŀ C' = {5, 15} B) B ŀ C' = {30, 40} C) B ŀ C' = + D) B ŀ C' = {25, 35} Answer: D 37) Let U = {5, 10, 15, 20, 25, 30, 35, 40} A = {5, 10, 15, 20} B = {25, 30, 35, 40} C = {10, 20, 30, 40}. Find A ŀ C . A) A ŀ C = {5, 15, 30, 40} B) A ŀ C = + C) A ŀ C = {10, 20} D) A ŀ C = {5, 10, 15, 20, 30, 40} Answer: C 38) Let U = {5, 10, 15, 20, 25, 30, 35, 40} A = {5, 10, 15, 20} B = {25, 30, 35, 40} C = {10, 20, 30, 40}. Find A' 1 C' A) A' 1 C' = + B) A' 1 C' = {25, 35} C) A' 1 C' = {5, 10, 15, 20, 25, 30, 35, 40} D) A' 1 C' = {5, 15, 25, 30, 35, 40} Answer: D 7

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    39) Let U = { 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 } X = { 4 , 6 , 8 , 10 , 12 , 14 } Y = { 4 , 5 , 6 , 7 , 8 , 9 } Z = { 5 , 7 , 8 , 9 , 12 , 13 , 14 }. Find ( X ŀ Y ) ŀ Z . A) ( X ŀ Y ) ŀ Z = { 8 } B) ( X ŀ Y ) ŀ Z = { 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 } C) ( X ŀ Y ) ŀ Z = { 4 , 5 , 6 , 7 , 8 , 9 , 10 , 12 , 13 , 14 } D) ( X ŀ Y ) ŀ Z = + Answer: A 40) Let U = {1, 2, 3, . . . } A = { 4 , 8 , 12 , 16 , . . . } B = { 12 , 24 , 36 , 48 , . . . }. Find A 1 B . A) A 1 B = ǹ B) A 1 B = U C) A 1 B = + D) A 1 B = B Answer: A 41) Let U = { n , p , q , r , s , t , u , v } A = { n , p , q , r } B = { n , q , s , u }. Find B - A . A) B - A = { s , u } B) B - A = + C) B - A = { n , p , q , r , s , u } D) B - A = { s , t , u , v } Answer: A 8

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    42) ƍ Draw a Venn diagram and shade the sections representing ǹ 1 Ǻ . A) B) C) D) Answer: D 43) Draw a Venn diagram and shade the sections representing ( ǹ 1 Ǻ ) ' . A) B) C) D) Answer: C 9

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    44) Draw a Venn diagram and shade the sections representing ǹ ŀ B' . A) B) C) D) Answer: A 45) A = {people who drive a compact car } and B = {people who drive a diesel vehicle}. Draw a Venn diagram of A ŀ B and write a sentence describing what the set represents. A) People who drive a compact car or a diesel vehicle 10

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    B) People who drive a diesel vehicle, but not a compact car . C) People who drive a diesel compact car . D) People who drive a compact car ,but not a diesel vehicle. Answer: C 11

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    46) Draw a Venn diagram and shade the sections representing A ŀ (B 1 C) A) B) C) D) Answer: D SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 47) Draw a Venn diagram and shade the sections representing ǹ ŀ ( Ǻ ŀ C ) ' Answer: 12

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    MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 48) Draw a Venn diagram and shade the sections representing (B 1 A) 1 A' . A) B) C) D) Answer: B 49) X = {students running cross country } , Y = {students swimming } , and Z = {students running track } . Draw a Venn diagram of Z - ( X 1 Y ) , and write a sentence describing what the set represents. A) Students running track but not running cross country or swimming . 13

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    B) Students not running cross country and not swimming . C) Students running track but not playing all three sports. D) Students running cross country , swimming and running track , or running track only. Answer: A 14

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    50) The table shows the students from Genius High School with the four highest GPAs from 2005 to 2007. Write the region(s) of the Venn diagram that would include Harry . (Note set X represents 2005 top-ranked students, set Y represents 2006 top-ranked students, and set Z represents 2007 top-ranked students.) Year 2005 2006 2007 Students Laura Carols Laura Kellyn Stefan Sasha Henry Harry Henry Harry Georg Harry A) Region II B) Region VI C) Region IV D) Region V Answer: D 51) Determine whether the two sets are equal. ( D 1 E ) ' and D ' 1 E ' A) not equal B) equal Answer: A 52) ƍ ƍ ƍ If U = { Bob , Ann , Mae , Eve , Dan , Kim , Tal , Vic }, A = { Ann , Eve , Dan , Kim }, and B = { Bob , Ann , Mae , Eve } find ( A 1 B ) and A ŀ B . A) Both are { Ann , Eve } B) Both are + C) Both are { Tal , Vic } D) Both are { Bob , Ann , Mae , Eve , Dan , Kim } Answer: C 15

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    53) ƍ ƍ ƍ If U = { Bob , Ann , Mae , Eve , Dan , Pat , Tal , Liz }, A = { Ann , Eve , Dan , Pat }, and B = { Bob , Ann , Mae , Eve } find ( A ŀ B ) and A 1 B . A) Both are { Bob , Mae , Eve , Dan , Pat } B) Both are + C) Both are { Ann , Eve } D) Both are { Tal , Liz } Answer: A SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 54) Determine whether the two sets are equal. ( A 1 B' ) ŀ C and ( A ŀ C ) 1 ( B' ŀ C ) Answer: equal 55) ƍ Determine whether the two sets are equal. A 1 ( B ŀ C ) ' and A ŀ ( B 1 C' ) Answer: not equal MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 56) Use the Venn diagram and find n ( A 1 B ) . A) n ( A 1 B ) = 2 B) n ( A 1 B ) = 9 C) n ( A 1 B ) = 7 D) n ( A 1 B ) = 5 Answer: C 57) Let U = { x x is a natural number < 15 } A = { x x is an odd natural number} B = { x x is a prime number}. Find n ( A 1 B ). Note: prime numbers are 2, 3, 5, 7 ,11, 13, 17, 19. A) n ( A 1 B ) = 12 B) n ( A 1 B ) = 7 C) n ( A 1 B ) = 8 D) n ( A 1 B ) = 2 Answer: C 16

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    58) In a survey of 18 college students, it was found that 11 were taking an English class, 6 were taking a math class, and 4 were taking both English and math. How many students were taking a math class only? A) 11 B) 2 C) 7 D) 5 Answer: B 59) In a survey of 29 instructors, it was found that 22 liked whiteboards, 11 liked blackboards, and 7 liked both. How many instructors did not like whiteboards? A) 14 B) 7 C) 3 D) 4 Answer: B 60) In a group of 53 children, 22 had a dog, 18 had a cat, and 6 had both a dog and a cat. How many children had neither a dog nor a cat as a pet? A) 31 B) 37 C) 12 D) 19 Answer: D 61) One weekend, there were 98 pizzas ordered for the sophomore dorm. That weekend 19 customers ordered their pizza with just pepperoni, 16 customers ordered their pizza with just sausage, 20 ordered theirs with just onions, 15 ordered theirs with pepperoni and sausage, 9 ordered theirs with sausage and onions, 17 ordered theirs with pepperoni and onions, and 2 ordered theirs with all three items. How many customers ordered their pizza with pepperoni or sausage (or both)? A) 72 B) 35 C) 50 D) 13 Answer: A 62) One weekend, there were 61 pizzas ordered for the sophomore dorm. That weekend 12 customers ordered their pizza with just pepperoni, 18 customers ordered their pizza with just sausage, 13 ordered theirs with just onions, 6 ordered theirs with pepperoni and sausage, 5 ordered theirs with sausage and onions, 4 ordered theirs with pepperoni and onions, and 2 ordered theirs with all three items. The remaining pizzas were cheese pizzas with no toppings. How many customers ordered at most two toppings on their pizza? A) 58 B) 15 C) 16 D) 59 Answer: D 63) Upon examining the contents of 38 backpacks, it was found that 23 contained a black pen, 27 contained a blue pen, and 21 contained a pencil, 15 contained both a black pen and a blue pen, 12 contained both a black pen and a pencil, 18 contained both a blue pen and a pencil, and 10 contained all three items. How many backpacks contained none of the three writing instruments? A) 2 B) 15 C) 11 D) 3 Answer: A 17

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    64) Upon examining the contents of 38 backpacks, it was found that 23 contained a black pen, 27 contained a blue pen, and 21 contained a pencil, 15 contained both a black pen and a blue pen, 12 contained both a black pen and a pencil, 18 contained both a blue pen and a pencil, and 10 contained all three items. How many backpacks contained exactly one of the three writing instruments? A) 3 B) 11 C) 2 D) 15 Answer: B 65) Upon examining the contents of 38 backpacks, it was found that 23 contained a black pen, 27 contained a blue pen, and 21 contained a pencil, 15 contained both a black pen and a blue pen, 12 contained both a black pen and a pencil, 18 contained both a blue pen and a pencil, and 10 contained all three items. How many backpacks contained exactly two of the three writing instruments? A) 11 B) 2 C) 15 D) 3 Answer: C 66) Which set is finite? A) {2, 4, 6, 8, 10, 12, . . .} B) { x x % ȃ and x < 100} C) { x x % ȃ and x is odd} D) { x x % ȃ and x > 100} Answer: B 67) Which set is infinite? A) + B) { x x is an improper fraction} C) {3, 5, 7, . . ., 99} D) { x x % ȃ and x < 20} Answer: B SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 68) Show that the set is an infinite set. { 6 , 12 , 18 , 24 , 30 , . . .} Answer: { 6 , 12 , 18 , 24 , 30 , ..., 6 n , ...} Ľ Ľ Ľ Ľ Ľ Ľ { 12 , 24 , 36 , 48 , 60 , ..., 12 n , ...} 69) Show that the set is an infinite set. { 0 , 4 , 8 , 12 , 16 , . . .} Answer: { 0 , 4 , 8 , 12 , 16 , ..., 4 n - 4 , ...} Ľ Ľ Ľ Ľ Ľ Ľ { 4 , 12 , 20 , 28 , 36 , ..., 8 n - 4 , ...} 18

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    70) Show that the set is an infinite set. 2 1 , 2 2 , 2 3 , 2 4 , 2 5 , ... Answer: 2 1 , 2 2 , 2 3 , ..., 2 n , ... Ľ Ľ Ľ Ľ 2 2 , 2 3 , 2 4 , ..., 2 n + 1 , ... 71) Show that the set is an infinite set. 1 10 , 1 100 , 1 1,000 , 1 10,000 , ... Answer: 1 10 , 1 100 , ..., 1 10 n , ... Ľ Ľ Ľ 1 100 , 1 10,000 , ..., 1 10 2 n , ... MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 72) Find the general term of the set. { -10 , -20 , -30 , -40 , -50 , . . .} A) -11 n + 1 B) -9 n – 1 C) -10 n D) n - 11 Answer: C SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 73) Find the general term of the set. 1 14 , 1 15 , 1 16 , 1 17 , 1 18 , ... Answer: 1 n + 13 74) The general term of the set 1 46 , 2 46 , 3 46 , 4 46 , 5 46 , ... is . Answer: n 46 19

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    MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 75) Find the general term of the set. { 9 , 12 , 15 , 18 , 21 , . . .} A) 2 n + 7 B) 9 n C) 4 n + 5 D) 3 n + 6 Answer: D ESSAY. Write your answer in the space provided or on a separate sheet of paper. 76) Show that the set of positive rational numbers with denominators 3 or 5 is a countable set. (Rational numbers are fractions with integers in the numerator and denominator.) Answer: One possibility: 1 2 3 4 5 6 ... Ľ Ľ Ľ Ľ Ľ Ľ 1 3 1 5 2 3 2 5 3 3 3 5 ... n ĺ n + 1 6 if n is odd n 6 if n is even 77) Show that the given set is countable. { 3 , 6 , 9 , 12 , 15 , ...} Answer: The set is countable because it can be put into one-to-one correspondence with the set of natural numbers. 1 2 3 4 5,..., n, ... Ľ Ľ Ľ Ľ Ľ Ľ 3 6 9 12 15 3 n , ... 20

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    MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Which sentence is not a statement? A) Ron got an A on the test. B) Stop that. C) 2 + 5 = 3 D) Mia lives in Los Angeles. Answer: B 2) Determine whether each sentence is a statement or not. i. He has blond hair. ii. He is not home. iii. The sky is brown. iv. Are you going to try again? A) Yes , No , No , No B) No , Yes , No , No C) No , No , Yes , No D) Yes , Yes , Yes , No Answer: D SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 3) Is the following sentence a statement? Neither Ben nor Alonzo is going camping. Answer: Yes. 4) State whether the sentence is a statement or not. Close the door. Answer: Not a statement MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 5) Classify each statement as simple or compound. i. Jeff's brother is two years old. ii. I am going to get a dog or a cat. iii. 4 + 1 = 4 iv. 2 × 0 = 0 A) Compound , Compound , Simple , Compound B) Simple , Compound , Simple , Simple C) Simple , Simple , Simple , Simple D) Compound , Compound , Compound , Compound Answer: B SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 6) Decide if the statement is simple or compound. I will go with you if and only if we are on time. Answer: Compound 1

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    MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 7) Which of the following is a simple statement? A) My dad is a plumber and an electrician. B) If he does his chores, he gets his allowance. C) 3 + 3 = 5 D) Neither food nor drink is allowed in that theater. Answer: C SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 8) Decide whether each statement is simple or compound. i. If you win the next round, you will be a finalist. ii. She is not feeling well. iii. 7 + 2 = 14 iv. He is taking history and economics. Answer: Compound, Compound, Simple, Compound MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 9) Identify the statement as a conjunction, disjunction, conditional, or biconditional. Rory will go to Yale, or she will go to Harvard. A) Conditional B) Biconditional C) Disjunction D) Conjunction Answer: C 10) Identify the statement as a conjunction, disjunction, conditional, or biconditional. If Raffi misses the goal, then we will lose the game. A) Conjunction B) Conditional C) Disjunction D) Biconditional Answer: B 11) Identify the quantifier in the statement as either universal or existential. There is a hair in my soup. A) Universal B) Existential Answer: B SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 12) Write the negation of the statement. The dog is spotted. Answer: The dog is not spotted. 2

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