1) A = {19, 20, 21, 22, 23} B = {18, 19, 20, 21, 22} 2) 2) 3) 3) A) {q, r, t, y, z} B) {r, s, t, y, z} C) {r, t, z} D) {q, s, u, v, x, y} 4) 4) 6) 6)

Transcription

1 Exam 1B Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Are the sets equivalent? 1) A = {19, 20, 21, 22, 23} 1) B = {18, 19, 20, 21, 22} A) Yes B) No 2) 2) A is the set of residents age 63 or older living in the United States B is the set of residents age 63 or older registered to vote in the United States A) Yes B) No Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}. List the elements in the set. 3) 3) (A' B) (A' C') A) {q, r, t, y, z} B) {r, s, t, y, z} C) {r, t, z} D) {q, s, u, v, x, y} 4) 4) (A B) (A C) A) {q, s, w, y} B) {r, t, v, x} C) {q, s, u, w, y} D) {q, s, u, w, y, z} 5) A' B 5) A) {s, u, w} B) {q, s, t, u, v, w, x, y} C) {q, r, s, t, v, x, y, z} D) {r, s, t, u, v, w, x, z} 6) 6) C A) { } B) {v, w, x, y, z} C) {q, s, y, z} D) {q, s, u, w, y} 7) (A B C)' 7) A) {q, s, u, w, z} B) C) {q, r, s, t, u, v, w, x, z} D) {r, t, v, x} 8) (A C)' 8) A) {q, r, s, t, u, v, w, x, y, z} B) {q, s, y, z} C) {q, r, s, t, u, v, x, z} D) {w, y}

2 Use the Venn diagram to list the elements of the set in roster form. 9) The set of students who studied Saturday 9) A) {Karen, Charly, Vijay} B) {Karen, Charly, Sam, Sophia} C) {Sam, Sophia} D) {Karen, Charly} Use the Venn diagram to list the elements of the set in roster form. 10) 10) (A B)' A) {13, 17} B) {18, 19} C) {11, 12, 14, 15, 16} D) {11, 12, 13, 14, 15, 16, 17} Express the symbolic statement ~p in words. 11) p: Lake Mead is one of the Great Lakes. 11) A) It is true that Lake Mead is one of the Great Lakes. B) Lake Mead is not one of the Great Lakes. C) It is not true that Lake Mead is not one of the Great Lakes D) Lake Mead is truly one of the Great Lakes. 12) p: No fifth graders play soccer. 12) A) All fifth graders play soccer. B) At least one fifth grader plays soccer. C) Not all fifth graders play soccer. D) No fifth grader does not play soccer. Determine whether the statement is true or false. 13) Bob {Bob, Carol, Ted, Alice} 13) 2

3 14) 14) {France, Germany, Switzerland} 15) 15) {Alice} {Bob, Carol, Ted, Alice} 16) 16) 38 {1, 2, 3,..., 40} List the elements in the set. 17) The set of the days of the week 17) A) {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Sunday} B) {Saturday, Sunday} C) {Tuesday, Thursday} D) {Friday, Monday, Saturday, Sunday, Thursday, Tuesday, Wednesday} Write a word description of the set. 18) {January, February, March, April, May, June, July, August, September, October, November, 18) December} A) days of the week B) days of the year C) months of the year D) seasons of the year Write the negation of the quantified statement. (The negation should begin with "all," "some," or "no.") 19) Some eagles are not birds. 19) A) All eagles are birds. B) All eagles are not birds. C) No eagles are birds. D) All birds are eagles. Calculate the number of subsets and the number of proper subsets for the set. 20) the set of natural numbers less than 10 20) A) 510; 511 B) 511; 510 C) 512; 511 D) 511; 512 Write the negation of the conditional statement. 21) If she can't water the lawn, I will. 21) A) She can water the lawn, and I can't. B) If she can water the lawn, I can't. C) She can't water the lawn, and I won't. D) She can't water the lawn, I can't. 3

4 Given that p and q each represents a simple statement, write the indicated symbolic statement in words. 22) p: Darren admires Zoe 22) q: Zoe admires Darren ~ (p q) A) It is not true that Darren admires Zoe and Zoe admires Darren. B) Darren admires Zoe but Zoe does not admire Darren. C) Darren does not admire Zoe, but Zoe admires Darren. D) Darren admires Zoe and Zoe admires Darren. Given that p and q each represents a simple statement, write the indicated compound statement in its symbolic form. 23) p: She drives at 80 mph. 23) q: She gets a speeding ticket. She drives at 80 mph or she does not get a speeding ticket. A) p q B) p ~ q C) p ~ q D) p ~ q 24) 24) p: The outside humidity is high. q: The basement dehumidifier is running. r: The basement is getting moldy. The outside humidity is high and the basement dehumidifier is running, or the basement is getting moldy. A) p (q r) B) (p q) ~ r C) p q r D) (p q) r Given that p and q each represents a simple statement, write the indicated symbolic statement in words. 25) p: The car has been repaired. 25) q: The kids are home. r: We will visit Aunt Tillie. ~ r (~ p ~ q) A) We will not visit Aunt Tillie if and only if the car has not been repaired or the kids are not home. B) If we visit Aunt Tillie, then the car has been repaired or the kids are home. C) If we will not visit Aunt Tillie, then the car has not been repaired and the kids are not home. D) If we will not visit Aunt Tillie, then the car has not been repaired or the kids are not home. Given that p and q each represents a simple statement, write the indicated compound statement in its symbolic form. 26) p: The outside humidity is high. 26) q: The basement dehumidifier is running. r: The basement is getting moldy. If the outside humidity is high, then the basement dehumidifier is running or the basement is not getting moldy. A) p (q ~ r) B) p (q r) C) p (q ~ r) D) p (q ~ r) Express the quantified statement in an equivalent way, that is, in a way that has exactly the same meaning. 27) Some falcons are not birds. 27) A) All falcons are birds. B) Some birds are not falcons. C) All falcons are not birds. D) Not all falcons are birds. 4

5 28) 28) Some buildings are garages. A) At least one building is a garage. B) There exists at least one garage that is a building. C) No buildings are garages. D) All garages are buildings. Determine whether the set is finite or infinite. 29) {x x N and x 1000} 29) A) Finite B) Infinite 30) 30) The set of natural numbers less than 1 A) Finite B) Infinite 31) 31) {x x N and x 100} A) Finite B) Infinite Use sets to solve the problem. 32) Results of a survey of fifty students indicate that 30 like red jelly beans, 29 like green jelly beans, 32) and 17 like both red and green jelly beans. How many of the students surveyed like no green jelly beans? A) 17 B) 30 C) 21 D) 38 Let p, q, r, and s represent the following statements: p: One plays hard. q: One is a guitar player. r: The commute to work is not long. s: It is not true that the car is working. Express the following statement symbolically. 33) 33) The car is working. A) ~s B) ~r C) r D) s Write the compound statement in symbolic form. Let letters assigned to the simple statements represent English sentences that are not negated. Use the dominance of connectives to show grouping symbols (parentheses) in symbolic statements. 34) If I do not like the song and I change the station then the DJ is not entertaining or I look for a CD to 34) play. A) ~p [(r ~q) s] B) (~p r) (~q s) C) [~p (r ~q)] s D) (p ~r) (q ~s) 5

6 Let p, q, and r represent the following simple statements: p: There is a blizzard outside. q: We do not have to go to school. r: We go sledding. First place parenthesis as needed before and after the most dominant connective and then translate the symbolic statement into English. 35) 35) ~r ~p ~q A) If we do not go sledding then there is not a blizzard outside, or we have to go to school. B) If we go sledding, then there is a blizzard outside or we do not have to go to school. C) If we go sledding then there is a blizzard outside, and we do not have to go to school. D) If we do not go sledding, then there is not a blizzard outside or we have to go to school. Express the set using the roster method. 36) {x x N and x is greater than 10} 36) A) {11,13,15,...} B) {11,12,13} C) {11,12,13,...} D) {10,11,12,...} 37) the set of odd natural numbers less than 17 37) A) {1, 3, 5,..., 17} B) {1, 3, 5,..., 15} C) {2, 4, 6,..., 16} D) {0, 1, 3, 5,..., 15} Write or in the blank so that the resulting statement is true. 38) {red, blue, green} {blue, green, yellow, black} 38) A) B) Determine if the set is the empty set. 39) {x x < 4 and x > 8} 39) A) Yes, it is the empty set. B) No, it is not the empty set. 40) 40) {0, } A) Yes, it is the empty set. B) No, it is not the empty set. Are the sets equal? 41) {42, 44, 46, 48, 50} = {44, 46, 48, 50} 41) A) Yes B) No Form the negation of the statement. 42) Oslo is not the capital of Brazil. 42) A) It is true that Oslo is not the capital of Brazil. B) It is not true that Oslo is not the capital of Brazil. C) It is true that Brazil is not the capital of Oslo. D) It is not true that Brazil is not the capital of Oslo. 6

7 Fill in the blank with either or to make the statement true. 43) Ontario the set of states in the United States 43) A) B) Consider below the branching tree diagram based on the number per 3000 American adults. Let T = the set of Americans who like classical music R = the set of Republicans who like classical music D = the set of Democrats who like classical music I = the set of Independents who like classical music Determine whether the statement is true or false. 44) 44) Let M = the set of Democratic men who like classical music W = the set of Democratic women who like classical music If x D, then x W. Let U = {1, 2, 4, 5, a, b, c, d, e}. Use the roster method to write the complement of the set. 45) A = {2, 4, b, d} 45) A) {1, 5, a, e} B) {1, 2, 4, 5, a, b, c, d, e} C) {1, 3, 5, a, c, e} D) {1, 5, a, c, e} Find the cardinal number for the set. 46) {x x is a day of the week that begins with the letter N} 46) A) 3 B) 0 C) 1 D) 2 List all the subsets of the given set. 47) {Siamese, domestic shorthair} 47) A) {Siamese, domestic shorthair}, {Siamese}, {domestic shorthair}, { } B) {Siamese, domestic shorthair}, {domestic shorthair}, { } C) {Siamese, domestic shorthair}, {Siamese}, {domestic shorthair}, D) {Siamese}, {domestic shorthair}, { } Determine whether the sentence is a statement. 48) Does Rose always act like that at a party? 48) A) statement B) not a statement 7

8 Use the Venn diagram shown to answer the question. 49) 49) Which regions represent set E'? A) II, III, V, VI B) VIII C) I, IV, VII, VIII D) II, V, VI Use,,, or both and to make a true statement. 50) {a, b} {z, a, y, b, x, c} 50) A) B) C) D) and 8