Questions 6 Consider the following argument: If Han obeys the rules, he keeps hi

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Questions 6

Consider the following argument:

If Han obeys the rules, he keeps his credit card.

Han does not obey the rules.

Therefore, he does not keep his credit card.

Create a truth table to determine whether the argument is true or false

Question 6 options:

  Let O = Han obeys the rules

Let K = Han keeps his credit card

O K   ~O OK

T T F T

T F F F

F T T T

F F T T

The Argument is true

Let O = Han obeys the rules

Let K = Han keeps his credit card

   O K   ~O OK

T T F T

T F T F

F T F T

F F T T

The Argument is true

Let O = Han obeys the rules

Let K = Han keeps his credit card

   O K   ~O OK

T T F T

T F T F

F T F T

F F T T

The Argument is false

Let O = Han obeys the rules

Let K = Han keeps his credit card

O K   ~O OK

T T F T

T F F F

F T T T

F F T T

The Argument is false

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Question 7 (1 point)

Using the following predicates

what is the best way to render the following predicate logic statement in English?

(x)[(C(x) & S(x)) (y)[M(y) & O(x,y)]]

Question 7 options:

For all cars that shine the exists a man who owns it

For each car that shines it implies that there exists a man who owns the car.

All shiney cars own a man.

All cars that shine imply that there exists a man who owns it.

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Question 8 (1 point)

Using the following predicates

what is the best way to render the following predicate logic statement in English?

(x)[(M(x) & (y)[C(y) & O(x,y)]) P(x)]

Question 8 options:

Each man that owns a shiney car is pleased

Every man who owns a car is pleased

There exists a car that all men own and they are pleased.

For all x that are men, there exists a y that is a car and the man owns the car which implies that the man is pleased.

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Question 9 (1 point)

Using the following predicates

what is the best way to render the following predicate logic statement in English?

(x)[(C(x) & ~(y)[M(y) & O(y,x)]]

Question 9 options:

There exists a car and not exists a man and the man owns the car.

No men own cars.

Cars do not own men.

There is a car that no-one owns.

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Question 10 (1 point)

Using the following predicates

what is the best way to render the following predicate logic statement in English?

(x)[(C(x) ~(y)[M(y) & O(x,y)]]

Question 10 options:

No man owns every car.

No car owns every man

No car owns a man

There exists a man that no car owns.

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Question 11 (1 point)

Using the following predicates

translate the following English statement into predicate logic:

All men who own cars wash them

Question 11 options:

x[M(x)^y(C(y)^O(x,y)]W(x,y)

x[M(x)^y(C(y)^O(x,y)]W(y,x)

x[M(x)^x(C(x)^O(x,y)]W(x,y)

x[M(x)^y(C(y)^O(y,x)]W(y,x)

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Question 12 (1 point)

Using the following predicates

translate the following English statement into predicate logic:

If a man washes a car, the car shines and the man is pleased

Question 12 options:

x[M(x)^C(y)^W(x,y)][S(x)^P(x)]

xy[M(x)^C(y)^W(x,y)][S(y)^P(x)]

xy[M(x)^C(y)^W(x,y)][S(x)^P(y)]

[M(x)^C(y)^W(x,y)][S(y)^P(x)]

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Question 13 (1 point)

Using the following predicates

translate the following English statement into predicate logic:

Every man owns a car that shines.

Question 13 options:

x(M(x))y[(C(y)^O(x,y)^S(y)]

xy(M(x)^(C(y)^O(x,y)^S(y))

x(M(x))y[(C(y)^O(x,y)^S(y)]

xy(M(x))[(C(y)^O(x,y)^S(y)]

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Question 14 (1 point)

Using the following predicates

translate the following English statement into predicate logic:

There is a car that does not shine and there is a man who owns it and who is not pleased.

Question 14 options:

x[C(x)^~S(x)]^y[M(y)^O(y,x)^~P(y)]

[C(x)^~S(x)]^[M(y)^O(y,x)^~P(y)]

x[C(x)^~S(x)]^y[M(y)^O(y,x)^~P(y)]

x[C(x)^~S(x)]^y[M(y)^O(x,y)^~P(y)]

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Question 15 (1 point)

Using the following predicates

translate the following English statement into predicate logic:

If a man is pleased, he owns a car and washes it.

Question 15 options:

x[M(x)^P(x)]y[C(y)^O(x,y)^W(x,y)]

x[M(x)^P(x)]y[C(y)^O(x,y)^W(x,y)]

x[M(x)^P(x)]y[C(y)^O(y,x)^W(y,x)]

x[M(x)^P(x)]^y[C(y)^O(x,y)^W(x,y)]

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  Let O = Han obeys the rules

Let K = Han keeps his credit card

O K   ~O OK

T T F T

T F F F

F T T T

F F T T

The Argument is true

Let O = Han obeys the rules

Let K = Han keeps his credit card

   O K   ~O OK

T T F T

T F T F

F T F T

F F T T

The Argument is true

Let O = Han obeys the rules

Let K = Han keeps his credit card

   O K   ~O OK

T T F T

T F T F

F T F T

F F T T

The Argument is false

Let O = Han obeys the rules

Let K = Han keeps his credit card

O K   ~O OK

T T F T

T F F F

F T T T

F F T T

The Argument is false

Explanation / Answer

6)
Let O = Han obeys the rules

Let K = Han keeps his credit card

     O    K    ~O     OK
------------------------------
     T    T     F      T
     T    F     F      F
     F    T     T      T
     F    F     T      T

The Argument is false

[The argument states that if Han obeys the rules, he {must} keep his credit card

but the argument does not state what will happen if Han does not obey the rules ]

7)
All four options are very colse to each other.
O(x,y) means x owns y
we know that x is shiney car or car that shines
y is a man

so the sentence structure becomes
all shiney cars own a man

so option c is closest

8)
Let us first consider this partial statement
(x)(M(x) & (y)[C(y) & O(x,y)])
states that for all men there exist a car that the men owns

now let us look into the complete statement
(x)[(M(x) & (y)[C(y) & O(x,y)]) P(x)]
initial part we know.
Now if we consider the complete statement as A impleis B,
the for A implies B is false only when A is true and B is false
if A is true, it states
there exist a man who owns a car
if B is false
the man is not pleased

so the statement is
it is false that there exist a man who owns a car who(man) is not pleased

so the final statement is Every man who owns a car is pleased

9)
let us first consider the partial statement:
~(y)[M(y) & O(y,x)] means it is false that there exist atleast a man who own x
OR
there exist no men who own x

now let us consider the complete statement
(x)[(C(x) & ~(y)[M(y) & O(y,x)]]
we are aware of the 2nd part of the statement, so the compelte statement states
there exist atleast one car x such that there exist no men who own x

so option d (There is a car that no-one owns.) is correct

Am sorry that I cannot solve other questions, since Chegg restricts us from answering more than 4 sub questions. I hope you understand. Please let me know in commtent section if you need more guidance on this. I shall be happy to help.

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