Questions 6 Consider the following argument: If Han obeys the rules, he keeps hi
ID: 3850054 • Letter: Q
Question
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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