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Chapter 3 ExamName___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is
a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol.
1) The car is in the garage and the bicycle is in the driveway. 1)
A) Compound; biconditional; ↔ B) Compound; conditional; →
C) Compound; conjunction; ∧ D) Compound; disjunction; ∨
2) The animal is a mammal if and only if it nurses its young. 2)
A) Compound; negation; ~ B) Compound; biconditional; ↔
C) Compound; conditional; → D) Compound; disjunction; ∨
3) If you forget to bring the book back to the library, you will have to pay a fine. 3)
A) Compound; biconditional; ↔ B) Compound; conditional; →
C) Simple statement D) Compound; conjunction; ∧
4) The apartment is rented or it is available. 4)
A) Compound; conjunction; ∧ B) Compound; biconditional; ↔
C) Compound; disjunction; ∨ D) Compound; conditional; →
5) The team leader has decided to take a vacation. 5)
A) Compound; conditional; → B) Compound; conjunction; ∧
C) Compound; negation; ~ D) Simple statement
6) The clown is not amusing. 6)
A) Simple statement B) Compound; disjunction; ∨
C) Compound; conjunction; ∧ D) Simple statement, negation; ~
7) It is false that whales are fish and bats are birds. 7)
A) Compound; biconditional; ↔ B) Compound; disjunction; ∨
C) Compound; negation; ~ D) Compound; conjunction; ∧
8) Trevor wanted to attend the meeting, but he had to go to the party. 8)
A) Compound; disjunction; ∨ B) Simple statement
C) Compound; conjunction; ∧ D) Compound; negation; ~
Write a negation of the statement.
9) Not all people like football. 9)
A) All people like football. B) Some people like football.
C) Some people do not like football. D) All people do not like football.
10) Everyone is asleep. 10)
A) None are asleep. B) Not everyone is asleep.
C) Everyone is not asleep. D) Everyone is awake.
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, 11) Some athletes are musicians. 11)
A) All athletes are musicians. B) No athletes are musicians.
C) All athletes are not musicians. D) Some athletes are not musicians.
12) No fifth graders play soccer. 12)
A) Some fifth graders play soccer. B) Fifth graders play soccer.
C) Everybody does not play soccer. D) Everybody plays soccer.
13) She earns more than me. 13)
A) She does not earn more than me. B) She does not earn less than me.
C) She earns the same as me. D) She earns less than me.
14) Some people donʹt like walking. 14)
A) All people like walking. B) Some people donʹt like driving.
C) Nobody likes walking. D) Some people like walking.
15) All dinosaurs were carnivores. 15)
A) All dinosaurs were not carnivores. B) No dinosaurs were carnivores.
C) Some dinosaurs were not carnivores. D) Some dinosaurs were carnivores.
16) Some photographs are not displayed at this exhibition. 16)
A) All photographs are displayed at this exhibition.
B) Some photographs are displayed at this exhibition.
C) All photographs are not displayed at this exhibition.
D) No photographs are displayed at this exhibition.
17) All squares are parallelograms. 17)
A) Some squares are not parallelograms. B) All squares are not parallelograms.
C) Some squares are parallelograms. D) No squares are parallelograms.
18) Some citizens obey traffic laws. 18)
A) Some citizens do not obey traffic laws. B) All citizens obey traffic laws.
C) No citizens do not obey traffic laws. D) No citizens obey traffic laws.
Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the
compound statements into symbols.
19) Jim does not play football and Michael does not play basketball. 19)
A) ~p ∧ ~q B) ~p ∨ ~q C) p ∧ q D) p ∨ q
20) Neither Jim plays football nor Michael plays basketball. 20)
A) ~(p ∧ q) B) p ∧ ~q C) ~p ∨ q D) ~(p ∨ q)
21) Jim does not play football and Michael plays basketball. 21)
A) ~p ∧ q B) ~(p ∧ q) C) p ∧ q D) ~p ∨ q
22) Jim does not play football or Michael plays basketball. 22)
A) p ∨ q B) p ∧ q C) ~p ∨ q D) ~(p ∨ q)
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, 23) It is not the case that Jim does not play football and Michael does not play basketball. 23)
A) ~p ∧ ~q B) ~(p ∨ q) C) ~(~p ∧ ~q) D) ~(~p ∨ ~q)
24) Jim does not play football or Michael does not play basketball. 24)
A) ~p ∨ ~q B) p ∧ q C) ~(p ∨ q) D) ~p ∧ ~q
25) Jim plays football and Michael plays basketball. 25)
A) p ∨ q B) p ∧ q C) ~p ∧ q D) p ∨ ~q
Write the compound statement in symbols.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ
q = ʺIʹll exercise.ʺ
26) If I eat too much, then Iʹll exercise. 26)
A) q → p B) p ∨ q C) p → q D) r → p
27) If I exercise, then I wonʹt eat too much. 27)
A) q → ~p B) p → q C) ~(p → q) D) r ∧ p
28) If the food is good, then I eat too much. 28)
A) p → r B) r ∧ p C) p → q D) r → p
29) If the food is good and if I eat too much, then Iʹll exercise. 29)
A) p → (r ∧ q) B) (r ∧ p) → q C) r ∧ (p → q) D) r → (p ∧ q)
30) If the food is good or if I eat too much, Iʹll exercise. 30)
A) (r ∧ p) → q B) r → p → q C) r → (p ∨ q) D) (r ∨ p) → q
31) If the food is not good, I wonʹt eat too much. 31)
A) ~(r → p) B) r → ~p C) ~p → ~r D) ~r → ~p
32) Iʹll exercise if I eat too much. 32)
A) p ∨ q B) q → p C) q ∧ p D) p → q
33) The food is good and if I eat too much, then Iʹll exercise. 33)
A) (r ∧ p) → q B) (r → p) ∨ q C) (r ∨ p) → q D) r ∧ (p → q)
34) Iʹll exercise if I donʹt eat too much. 34)
A) ~(p → q) B) ~p ∧ q C) ~p ∨ q D) ~p → q
35) If I exercise, then the food wonʹt be good and I wonʹt eat too much. 35)
A) q → (~r ∧ ~p) B) (q ∧ ~r) → ~p C) q → ~(r ∧ p) D) ~(r ∧ p) → q
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, Convert the compound statement into words.
36) p = ʺHer name is Lisa.ʺ 36)
q = ʺShe lives in Chicago.ʺ
~p
A) Her name is Lisa. B) She does not live in Chicago.
C) Her name is not Lisa. D) It is true her name is Lisa.
37) p = ʺBabies eat bananas.ʺ 37)
q = ʺBabies wear plastic bibs.ʺ
p∨q
A) Babies eat bananas and babies wear plastic bibs.
B) Babies eat bananas or babies do not wear plastic bibs.
C) Babies eat bananas or babies wear plastic bibs.
D) Babies wear plastic bibs and babies eat bananas.
38) p = ʺPeople buy large houses.ʺ 38)
q = ʺFossil fuels pollute the air.ʺ
q∧p
A) Fossil fuels pollute the air and people buy large houses.
B) Fossil fuels pollute the air or people buy large houses.
C) It is not the case that fossil fuels pollute the air and people buy large houses.
D) People buy large houses and fossil fuels do not pollute the air.
39) p = ʺStudents are happy.ʺ 39)
q = ʺTeachers are happy.ʺ
~(p ∨ ~q)
A) It is not the case that students are happy or teachers are not happy.
B) Students are not happy and teachers are not happy.
C) Students are not happy or teachers are not happy.
D) It is not the case that students are happy and teachers are not happy.
40) p = ʺThe food tastes delicious.ʺ 40)
q = ʺWe eat a lot.ʺ
r = ʺNobody has dessert.ʺ
(q ∨ p) ∧ r
A) We eat a lot or the food tastes delicious or nobody has dessert.
B) We eat a lot and the food tastes delicious or nobody has dessert.
C) We eat a lot or the food tastes delicious and nobody has dessert.
D) We do not eat a lot or the food tastes delicious and nobody has dessert.
41) p = ʺThe food tastes delicious.ʺ 41)
q = ʺWe eat a lot.ʺ
r = ʺNobody has dessert.ʺ
~q ∨ (p ∧ r)
A) We do not eat a lot and the food tastes delicious and nobody has dessert.
B) We eat a lot or the food tastes delicious and nobody has dessert.
C) We do not eat a lot or the food tastes delicious and nobody has dessert.
D) We do not eat a lot or the food tastes delicious or nobody has dessert.
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