Deck 3: The Nature of Logic

Question 1

Using AND-gates, OR-gates, and NOT-gates, design a circuit that would find the truth values for the sentence. ​
​ ​
(a) ​
(b) ​
(c) ​

A) b
B) c
C) a

Answer 1

a

Question 2

What does the circuit symbol in the figure mean? ​ ​

A) light
B) switch
C) battery (or power source)

Answer 2

battery (or power source)

Question 3

Explain when the light on a circuit is off. ​

A) Circuit is complete when light is on
B) Circuit is incomplete when light is off

Answer 3

Circuit is incomplete when light is off

Question 4

Using gates, design a circuit for the conditional statement. ​
​ ​
(a) ​
(b) ​
(c) ​

A) a
B) b
C) c

Question 5

Using switches, design a circuit that would find the truth values for the statement. ​ ​
(a) (b) (c) ​

A) a
B) b
C) c

Question 6

First build a truth table and then design a circuit using switches that would find the truth values for the statement. ​ ​

A)
B)
C)
D)
E)

Question 7

What does the circuit symbol in the figure mean? ​ ​

A) Battery
B) NOR-gate
C) AND-gate
D) Light
E) Switch

Question 8

Alfie, Betty, and Connie are the members of a Senate committee. Design a circuit that will output yea or nay depending on the way the majority of the committee members voted. Let the committee members be a, b, and c, respectively. ​
(a) (b) (c) ​

A) c
B) b
C) a

Question 9

Using switches, design a circuit that would find the truth values for the statement. ​
​
​ ​
(a) (b) (c) ​

A) c
B) b
C) a

Question 10

What does the circuit symbol in the figure mean? ​ ​

A) battery (or power source)
B) switch
C) light

Question 11

What does the circuit symbol in the figure mean? ​ ​

A) AND-gate
B) NOT-gate
C) OR-gate

Question 12

What does the circuit symbol in the figure mean? ​ ​

A) AND-gate
B) Switch
C) Light
D) NOT-gate
E) Battery

Question 13

What does the circuit symbol in the figure mean? ​ ​

A) Battery
B) Switch
C) AND-gate
D) Light
E) OR-gate

Question 14

What does the circuit symbol in the figure mean?

A) NOT-gate
B) OR-gate
C) AND-gate

Question 15

What does the circuit symbol in the figure mean? ​ ​

A) OR-gate
B) Switch
C) Battery
D) AND-gate
E) NOT-gate

Question 16

What does the circuit symbol in the figure mean?

A) NOT-gate
B) OR-gate
C) AND-gate

Question 17

What does the circuit symbol in the figure mean? ​ ​

A) AND-gate
B) NOT-gate
C) Switch
D) Battery
E) OR-gate

Question 18

Using switches, design a circuit that would find the truth values for the statement. ​ ​ ​

A) c
B) b
C) a

Question 19

What does the circuit symbol in the figure mean? ​ ​

A) Battery
B) AND-gate
C) OR-gate
D) NOT-gate
E) Switch

Question 20

What does the circuit symbol in the figure mean? ​ ​

A) switch
B) battery (or power source)
C) light

Question 21

Using AND-gates, OR-gates, and NOT-gates, design a circuit that would find the truth values for the sentence. ​ ​
Select the correct circuit.
​

A)
B)
C)

Question 22

Find a so that the statement is true.

A) 1
B) 4
C) 0
D) 2
E) 3

Question 23

Find a so that the statement is true.

A) 0
B) 5
C) 4
D) 7
E) 3

Question 24

Find a so that the statement is true.

A) 2
B) 0
C) 5
D) 3
E) 4

Question 25

Find a so that the statement is true.

A) 6
B) 2
C) 0
D) 3
E) 1

Question 26

Using switches, design a circuit that would find the truth values for the statement. ​ ​
Select the correct circuit.
​

A)
B)
C)

Question 27

Find a so that the statement is true.

A) 0
B) 6
C) 5
D) 3
E) 4

Question 28

Find a so that the statement is true. ​ ​

A) 0
B) 3
C) 2
D) 4
E) 1

Question 29

Using switches, design a circuit that would find the truth values for the statement. ​ ​
Select the correct circuit.
​

A)
B)
C)

Question 30

Alfie, Betty, and Clyde are the members of a Senate committee. Design a circuit that will output yea or nay depending on the way the majority of the committee members voted. Let the committee members be a, b, and c, respectively. ​
Select the correct circuit.
​

A)
B)
C)

Question 31

Find a so that the statement is true.

A) 3
B) 5
C) 0
D) 6
E) 2

Question 32

Find a so that the statement is true.

A) 5
B) 6
C) 0
D) 4
E) 2

Question 33

Find a so that the statement is true.

A) 3
B) 4
C) 5
D) 2
E) 0

Question 34

Explain when the light on a circuit is on.
​
Circuit is __________ (complete, incomplete) when light is __________ (on, off).

Question 35

Find a so that the statement is true.

A) 4
B) 7
C) 6
D) 0
E) 3

Question 36

Find a so that the statement is true.

A) 5
B) 7
C) 0
D) 3
E) 6

Question 37

Using gates, design a circuit for the conditional statement. ​ ​
Select the correct circuit.
​

A)
B)
C)

Question 38

Find a so that the statement is true.

A) 5
B) 3
C) 4
D) 2
E) 0

Question 39

Using switches, design a circuit that would find the truth values for the statement. ​ ​
Select the correct circuit.

A)
B)
C)

Question 40

Find a so that the statement is true.

A) 2
B) 3
C) 0
D) 5
E) 4

Question 41

Find a so that the statement is true. a = __________

Question 42

Find a so that the statement is true. a = __________

Question 43

Find a so that the statement is true. a = __________

Question 44

Find a so that the statement is true. a = __________

Question 45

Suppose I have three bags, one with two peaches, another with two plums, and a third mixed bag with one peach and one plum. Now I give the bags (in mixed-up order) to Alice, Annie, and Nancy. I tell the three to look into their bags and that I want each to make a statement about the contents of her bag, but I want them to lie. Here is what they say: ​
Alice : I have two peaches.
Annie : I have two plums.
Nancy : I have one peach and one plum.
​
Now here is the game. I want you to develop a strategy of asking one of the three to reach into their bag and pull out one fruit and show it to you. The fruit is then returned to the bag and you ask another to do the same thing. Continue until you can deduce which bag is the mixed bag. What is the minimum possible number of necessary moves?
​

A) Only one question is necessary: Ask Nancy (who falsely claimed to have the mixed bag) to pull out one fruit. Suppose she pulls out a peach; this means she has the bag containing two peaches. Then, Alice, who falsely claimed two peaches, must have two plums. This leaves Annie with the mixed bag. Suppose she pulls out a plum; this means she has the bag containing two plums. Then, Annie, who falsely claimed two plums, must have two peaches. This leaves Alice with the mixed bag.
​
B) Only one question is necessary: Ask Annie (who falsely claimed to have the mixed bag) to pull out one fruit. Suppose she pulls out a peach; this means she has the bag containing two peaches. Then, Alice, who falsely claimed two peaches, must have two plums. This leaves Nancy with the mixed bag. Suppose she pulls out a plum; this means she has the bag containing two plums. Then, Nancy, who falsely claimed two plums, must have two peaches. This leaves Alice with the mixed bag.
​
C) Only one question is necessary: Ask Nancy (who falsely claimed to have the mixed bag) to pull out one fruit. Suppose she pulls out a peach; this means she has the bag containing two peaches. Then, Annie, who falsely claimed two peaches, must have two plums. This leaves Alice with the mixed bag. Suppose she pulls out a plum; this means she has the bag containing two plums. Then, Alice, who falsely claimed two plums, must have two peaches. This leaves Annie with the mixed bag.
​

Question 46

Find a so that the statement is true.

A) 7
B) 4
C) 5
D) 6
E) 0

Question 47

Find a so that the statement is true. a = __________

Question 48

Suppose you are given 12 coins, one of which is counterfeit and weighs a little more or less than the real coins. Using a two-pan balance scale, what is the minimum number of weighings necessary to find the counterfeit coin? ​

A) 7 weighings
B) 3 weighings
C) 1 weighings
D) 4 weighings
E) 6 weighings

Question 49

Find a so that the statement is true.

A) 6
B) 0
C) 5
D) 8
E) 7

Question 50

A fox, hunting for a morsel of food, spotted a huge bear about 175 yards due east of him. Before the hunter could become the hunted, the crafty fox ran due north for 175 yards but then realized the bear had not noticed him. Thus he stopped and remained hidden. At this point the bear was due south of the fox. What was the color of the bear? ​

A) Purple
B) White
C) Brown
D) Black
E) Green

Question 51

Find a so that the statement is true. a = __________

Question 52

Find a so that the statement is true.

A) 6
B) 5
C) 0
D) 3
E) 4

Question 53

I visited a beautiful flower garden yesterday and counted exactly 50 flowers. Each flower was either white or orange, and the flowers were not all the same color. My friend made the following observation: No matter which two flowers you might have picked, at least one was bound to be white. From this can you determine how many were white and how many were orange? ​

A) 1 orange flower, 49 white flower(s)
B) 1 white flower, 49 orange flower(s)
C) 32 orange flower(s), 18 white flower(s)
D) 24 orange flower(s), 26 white flower(s)
E) 26 orange flower(s), 24 white flower(s)

Question 54

Four boys were playing marbles; their names were Gary, Henry, John, and Alice. One of the boys had 9 marbles, another had 15, and each of the other two had 12. Their ages were 3, 10, 17, and 18, but not respectively. Gary shot before Henry and Alice. Alice was older than the boy with 15 marbles. Henry had fewer than 15 marbles. Alice shot before Henry. John shot after Henry. If John was 10 years old, he did not have 15 marbles. Gary and Alice together had an even number of marbles. The youngest boy was not the one with 15 marbles. If Henry had 12 marbles, he wasn't the youngest. The 10-year-old shot after the 17-year-old. How old was each boy? ​

A) John - 3, Henry - 17, Gary - 10, Alice - 18.
B) John - 10, Henry - 3, Gary - 17, Alice - 18.
C) John - 17, Henry - 18, Gary - 3, Alice - 10.
D) John - 3, Henry - 10, Gary - 17, Alice - 18.
E) John - 17, Henry - 10, Gary - 3, Alice - 18.

Question 55

I have a habit of getting up before the sun rises. My socks are all mixed up in the drawer, which contains 20 blue and 18 black socks. I reach into the drawer and grab some socks in the dark. How many socks minimum do I need to take from the drawer to be sure that I have a matched pair? ​

A) 18 socks
B) 21 socks
C) 2 socks
D) 3 socks
E) 19 socks

Question 56

Find a so that the statement is true.

A) 8
B) 0
C) 7
D) 5
E) 6

Question 57

Find a so that the statement is true.

A) 0
B) 4
C) 7
D) 5
E) 6

Question 58

I have a habit of getting up before the sun rises. My socks are all mixed up in the drawer, which contains 8 blue and 18 grey socks. I reach into the drawer and grab some socks in the dark. How many socks do I need to take from the drawer to be sure that I have a matched pair?
​
__________ socks

Question 59

Find a so that the statement is true. a = __________

Question 60

Find a so that the statement is true. a = __________

Question 61

Find a so that the statement is true. a = __________

Question 62

Find a so that the statement is true. a = __________

Question 63

Find a so that the statement is true. a = __________

Question 64

Determine whether the argument in the problem below is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. ​
If , then . Therefore, .
​

A) valid; indirect
B) valid; direct
C) valid; transitive
D) invalid; direct
E) invalid; indirect

Question 65

Find a so that the statement is true. a = __________

Question 66

Find a so that the statement is true. a = __________

Question 67

Suppose you are given 12 coins, one of which is counterfeit and weighs a little more or less than the real coins. Using a two-pan balance scale, what is the minimum number of weighings necessary to find the counterfeit coin?
​
__________ weighings

Question 68

Suppose I have three bags, one with two peaches, another with two plums, and a third mixed bag with one peach and one plum. Now I give the bags (in mixed-up order) to Alice, Betty, and Connie. I tell the three to look into their bags and that I want each to make a statement about the contents of her bag, but I want them to lie. Here is what they say:
​
Alice : I have two peaches.
Betty : I have two plums.
Connie : I have one peach and one plum.
​
Now here is the game. I want you to develop a strategy of asking one of the three to reach into their bag and pull out one fruit and show it to you. The fruit is then returned to the bag and you ask another to do the same thing. Continue until you can deduce which bag is the mixed bag. What is the minimum possible number of necessary moves? Explain.

Question 69

Find a so that the statement is true. a = __________

Question 70

Four boys were playing marbles; their names were Bob, Harry, Iggi, and Alice. One of the boys had 9 marbles, another had 15, and each of the other two had 12. Their ages were 3, 10, 17, and 18, but not respectively. Bob shot before Harry and Alice. Alice was older than the boy with 15 marbles. Harry had fewer than 15 marbles. Alice shot before Harry. Iggi shot after Harry. If Iggi was 10 years old, he did not have 15 marbles. Bob and Alice together had an even number of marbles. The youngest boy was not the one with 15 marbles. If Harry had 12 marbles, he wasn't the youngest. The 10-year-old shot after the 17-year-old. How old was each boy?
__________ was 3, __________ was 10, __________ was 17, __________ was 18

Question 71

I visited a beautiful flower garden yesterday and counted exactly 60 flowers. Each flower was either white or purple, and the flowers were not all the same color. My friend made the following observation: No matter which two flowers you might have picked, at least one was bound to be white. From this can you determine how many were white and how many were purple?
​
__________ white flower(s) and __________ purple flower(s)

Question 72

Determine whether the argument in the problem below is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. Assume that if a number is odd, then it is not even.
​
If a³ is even, then a must be even.
A is odd.
Therefore, ​a³ is odd.
​

A) invalid; false chain
B) invalid; direct
C) invalid; indirect
D) valid; indirect
E) valid; direct

Question 73

Find a so that the statement is true. a = __________

Question 74

Find a so that the statement is true. a = __________

Question 75

Find a so that the statement is true. a = __________

Question 76

A fox, hunting for a morsel of food, spotted a huge bear about 200 yards due east of him. Before the hunter could become the hunted, the crafty fox ran due north for 200 yards but then realized the bear had not noticed him. Thus he stopped and remained hidden. At this point the bear was due south of the fox.
​
The color of the bear was __________.

Question 77

Daniel Kilraine was killed on a lonely road, two miles from Pontiac, at 3:30
A.M. on March 3, 1997. Henry, Curly, Slim, Mickey, and The Kid were arrested a week later in Detroit and questioned. Each of the five made four statements, three of which were true and one of which was false. One of these men killed Kilraine. Who dunit? Their statements were:
Henry : "I was in Chicago when Kilraine was murdered. I never killed anyone. The Kid is the guilty man. Mickey and I are pals."
Curly : "I did not kill Kilraine. I never owned a revolver in my life. The Kid knows me. I was in Detroit the night of March 3rd."
Slim : "Curly lied when he said he never owned a revolver. The murder was committed on March 3rd. One of us is guilty. Henry was in Chicago at the time."
Mickey : "I did not kill Kilraine. The Kid has never been in Pontiac. I never saw Henry before. Curly was in Detroit with me on the night of March 3rd."
The Kid : "I did not kill Kilraine. I have never been in Pontiac. I never saw Curly before. Henry lied when he said I am guilty."
__________ committed the murder.

Question 78

Find a so that the statement is true. a = __________

Question 79

Determine whether the argument in the problem below is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. ​
If I inherit $1,100, I will buy you a cookie.
I inherit $1,100.
Therefore, I will buy you a cookie.
​

A) valid; direct
B) invalid; false chain
C) invalid; indirect
D) valid; indirect
E) invalid; direct

Question 80

Explain what we mean by indirect reasoning. ​

A)
B)
C)
D)
E) none of these