2. How many subsets are there in D={3, 4, 7, 8, 11, 14, 15, 16, 22}? How many proper subsets?
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1 Math 1332 Review for Exam 1 This review in and of itself does not prepare you for Exam 1. Make sure you have also done the suggested homework, online homework, and in-class quizzes. Exam 1: 2.1, 2.2, 2.3, 2.4, 2.5, 3.1, 3.2, 3.3, 3.4, 3.6 Chapter 2 (2.1, 2.2, 2.3, 2.4, 2.5) review questions (random order): 1. Express the following set in roster/list notation: A = {x x N and x < 10} 2. How many subsets are there in D={3, 4, 7, 8, 11, 14, 15, 16, 22}? How many proper subsets? 3. Determine whether the following pairs of sets are equal, equivalent, both, or neither. (a) A={lions, tigers, bears} (b) C={red, blue, yellow} B={bears, lions, tigers} D={nose, eye, mouth} 4. Determine TRUE or FALSE for each of the following: (a) {penny} {penny, nickel, dime, quarter} (b) { } = { } (c) {a,b,c} {b,c,a} (d) {3, 4} {1, 2, 3, 4} (e) {$,@,#} {@,#,$} 5. List all subsets for B={dog, cat} 6. Given A={#,m, 3} and B={5,d}, determine (a) A B (b) B B 7. The Poage s are putting a pool in and can either install the base model offered by the pool company or add any of the following options: automatic pool cleaner, solar cover, waterfall, hot tub, fountain, slide, diving board. How many different variations of the pool are possible? 8. If D = {a,b,c} Is a an element of D? Is b a subset of D? Is {c} a subset of D? Is D a subset of D? 9. Fleet Foot Racing interviewed 150 long-distance runners to determine the type of races in which they participated. The following information was determined: 102 participated in a marathon 93 participated in a triathlon 55 participated in both a marathon and a triathlon. How many people surveyed participated in (a) only a marathon? (b) a marathon or a triathlon (c) neither a marathon or a triathlon?
2 10. If A B and B C, must A C? 11. Let U = {x x is a student at Blinn College} with subsets A = {x x is a female} B = {x x rides the bus} C = {x x is taking a math class} Describe each of the following sets in words: (a) A B C (b) A C (B C) (c) (A B C C C ) 12. A survey was conducted of 100 people who visited the local health clinic today. Fill in the Venn diagram completely, based upon the following results. (NOTE: 2 numbers have been filled in for you) 44 did not have a cough 35 had a sore throat and runny nose 57 had a runny nose 31 had a cough and runny nose 22 did not have a sore throat or runny nose 13. List all subsets for 14. If A B and B C, must A C? 15. Use the Venn diagram to the right to list the following set of elements in roster notation. (a) A C (b) A B C (c) A B C (d) (A B) C (e) (A B) C (f) B A (g) A C B (h) A C B C (i) A C B C 16. The results of a survey of 50 customers at a pet supply store found 26 owned cats, 35 owned turtles, and 15 owned both cats and turtles. (a) How many owned cats or turtles? (b) How many owned only a cat? (c) How many owned neither a cat nor a turtle? 17. In a survey asked of 75 students this morning, 59 said they ate breakfast, 48 said they ate breakfast AND read the Battalion, and 7 said they didn't do either of these things. How many students surveyed read the Battalion?
3 18. Express the following set in set-builder notation: B = {5, 10, 15, 20, 25, } 19. At a Halloween party some of the guests brought cookies, drinks, or candy. Fill in the Venn (a) Diagram below according to the following information. 5 guest brought cookies, candy and drinks 19 guests brought exactly 2 items 21 guests brought drinks 20 guests did not bring cookies 8 guests brought only candy 2 guests did not bring a drink or candy 5 guests brought only cookies and drinks 11 guests brought drinks and candy (b) How many total people were invited? (c) How many did not bring anything? (d) How many brought cookie or candy, but not drinks? 20. A survey of 85 shoppers reveals that in the past week, 25 bought pop-tarts, 41 bought cereal, and 19 bought both pop-tarts and cereal. How many of the shoppers bought EXACTLY one of these two items? 21. Using the Venn diagram to the right, list the sets below in roster notation. (a) A B C (b) (A B) C (c) C (B A) (d) (A B) C C (e) A (B C) C (f) B C (A C C ) 22. Use Set notation with Union, Intersection, and Compliments to describe the shaded area for each of the Venn diagrams below. (a) (b) (c)
4 23. Ninety-five people were surveyed to see which characters they liked from the TV show FRIENDS. Based upon the following results, how many people said they liked ONLY liked Ross? 42 people did NOT like Ross 38 people liked Joey and Ross 71 people liked Monica 10 people like Monica and Ross, but not Joey 16 people liked ONLY Monica 21 people liked Joey, Monica, and Ross 1 person did not like any of them Chapter 3 (3.1, 3.2, 3.3, 3.4, 3.6) review questions (random order): 24. Write the negation for each of the following statements: (a) Some frogs do not jump. (b) All houses have doors. (c) No unicorns live in College Station. (d) Some vitamins contain sugar. 25. Is the following syllogism valid or invalid? All marigolds are annuals. Some tulips are annuals. Some tulips are marigolds. 26. Let p: Tanner has Snapchat q: Tanner has Instagram Write the following compound statements in words: (a) ~p q (b) p ~q (c) ~ (q p) 27. Construct a truth table for the following statement: ~(p ~q) p q ~(p ~q) 28. Construct a truth table for (q ~r) p 29. Write the Contrapositive for If Grannie can t babysit, then we do not go on a date.
5 30. Let p: It is flooding outside. q: School has been cancelled. r: The electricity is working. Write the following statements in symbolic form: (a) It is not flooding outside if and only if the electricity is not working, or school has not been cancelled. (b) If the electricity is working, then it is not flooding and school has not been cancelled. 31. Construct a truth table for ~p (q r) 32. Is the following syllogism valid or invalid? All dachshunds are mean. Sport is a dachshund Sport is mean. 33. Let p: Leslie made pizza q: ReAnna made salad r: Patrice did not burn the cookies Write the statement in symbolic form and construct a truth table: Leslie made pizza or ReAnna made salad, but Patrice did not burn the cookies. 34. Is the following syllogism valid or invalid? All dachshunds are mean. Sport is a mean Sport is a dachshund 35. NOTE: p is true, q is false, and r is true. Determine the truth value of each of the following: (a) (p ~q) ~r (b) ~p (~q ~r) 36. Let p: Apple starts with the letter A q: MATH is a 4-letter word r: Navasota is the capital of Texas Write in symbolic form and determine the truth value for: Navasota is the capital of Texas and MATH is not a 4-letter word, or Apple starts with the letter A. 37. Use a truth table to determine whether the following two statements are equivalent: ~(p q) and p ~q
6 38. Construct a truth table for (p q) p 39. Construct a truth table for (~p q) r 40. Write the converse for If Bob is the director, then Larry is the actor. 41. Is the following syllogism valid or invalid? Some kids love pancakes. All kids who love pancakes love syrup. Some kids love syrup. 42. Construct a truth table and determine if the statement is a tautology, self-contradiction, or neither: (~p q) ~q 43. Construct a truth table and determine if the statement is an implication. r (~p ~q) 44. Write the inverse for If the trees are blooming, then the grass does not grow. 45. Is the following syllogism valid or invalid? No scarecrows are tin men. No tin men are lions. No scarecrows are lions. 46. If p is true, q is false, and r is false, find the truth value of: (a) ~[p (q r)] (b) ~[(p q) (p ~r)] 47. Write the converse for If the house is rocking, then don t bother knocking. 48. Is the following syllogism valid or invalid? All rainy days are cloudy. Today it is cloudy. Today is a rainy day. 49. Is the following syllogism valid or invalid? No Casting Crowns are Newsboys. Some Newsboys are from DC Talk. No Casting Crowns are from DC Talk. 50. Write the inverse for If the road is flooding, then I turn my car around.
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