How to write “There is at least 2 Cars are not the same Colour” in logic
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I would like to know how to write “At least 2 Cars are not the same Colour” in logic.
I know that "at least two cars" can be defined as ∃x(C(x)∧∃y(C(x)∧y≠x)). is that right? What's next then
Also, how to write "himself/herself" in logic? For example "nobody is better than himself/herself".
Appreciate for any help.
logic predicate-logic logic-translation
edited Dec 10 '18 at 18:18
Bram28
61.6k44793
asked Dec 10 '18 at 11:02
BaivarasBaivaras
6
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add a comment |
$begingroup$
I would like to know how to write “At least 2 Cars are not the same Colour” in logic.
I know that "at least two cars" can be defined as ∃x(C(x)∧∃y(C(x)∧y≠x)). is that right? What's next then
Also, how to write "himself/herself" in logic? For example "nobody is better than himself/herself".
Appreciate for any help.
logic predicate-logic logic-translation
edited Dec 10 '18 at 18:18
Bram28
61.6k44793
asked Dec 10 '18 at 11:02
BaivarasBaivaras
6
$endgroup$
add a comment |
$begingroup$
I would like to know how to write “At least 2 Cars are not the same Colour” in logic.
I know that "at least two cars" can be defined as ∃x(C(x)∧∃y(C(x)∧y≠x)). is that right? What's next then
Also, how to write "himself/herself" in logic? For example "nobody is better than himself/herself".
Appreciate for any help.
logic predicate-logic logic-translation
edited Dec 10 '18 at 18:18
Bram28
61.6k44793
asked Dec 10 '18 at 11:02
BaivarasBaivaras
6
$endgroup$
I would like to know how to write “At least 2 Cars are not the same Colour” in logic.
I know that "at least two cars" can be defined as ∃x(C(x)∧∃y(C(x)∧y≠x)). is that right? What's next then
Also, how to write "himself/herself" in logic? For example "nobody is better than himself/herself".
Appreciate for any help.
logic predicate-logic logic-translation
logic predicate-logic logic-translation
edited Dec 10 '18 at 18:18
Bram28
61.6k44793
asked Dec 10 '18 at 11:02
BaivarasBaivaras
6
edited Dec 10 '18 at 18:18
Bram28
61.6k44793
asked Dec 10 '18 at 11:02
BaivarasBaivaras
6
edited Dec 10 '18 at 18:18
Bram28
61.6k44793
edited Dec 10 '18 at 18:18
Bram28
61.6k44793
edited Dec 10 '18 at 18:18
Bram28
61.6k44793
61.6k44793
asked Dec 10 '18 at 11:02
BaivarasBaivaras
6
asked Dec 10 '18 at 11:02
BaivarasBaivaras
6
asked Dec 10 '18 at 11:02
BaivarasBaivaras
6
6
add a comment |
add a comment |
1 Answer
1
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oldest
votes
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Suppose $C(x)$ denotes the colour $C$ of a car $x$. To translate "At least 2 cars are not the same colour" we could say "there are cars $x$ and $y$ that are not identical such that $C(x) ne C(y)$". In formal logic notation this is:
$exists space x,y space left( (space x ne y) land (space C(x) ne C(y)) right)$
or, without using $ne$, as follows:
$exists space x,y space left( lnot (space x = y) land lnot(space C(x) = C(y)) right)$
In fact, the qualification $x ne y$ is redundant, since $C(x) ne C(y) Rightarrow x ne y$. So we can simplify this to:
$exists space x,y space left(lnot(C(x) = C(y)) right)$
For the second part, if $B(x,y)$ denotes "$x$ is better than $y$" then "nobody is better than himself/herself" can be expressed as "there is no person $x$ such that $B(x,x)$". In formal logic notation this is:
$nexists space x space B(x,x)$
or
$forall space x space lnot B(x,x)$
answered Dec 10 '18 at 11:51
gandalf61gandalf61
8,481725
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The answer is a bit misleading since you do not use boolean constants, but use colon and comma. This is at most just a suggestion how to write a correct formula, or an abbreviation of such. Yet not a formal logic notation.
$endgroup$
– Mad Hatter
Dec 10 '18 at 12:18
1
$begingroup$
@MadHatter I have changed the notation.
$endgroup$
– gandalf61
Dec 10 '18 at 13:50
add a comment |
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1 Answer
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1 Answer
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active
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active
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active
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$begingroup$
Suppose $C(x)$ denotes the colour $C$ of a car $x$. To translate "At least 2 cars are not the same colour" we could say "there are cars $x$ and $y$ that are not identical such that $C(x) ne C(y)$". In formal logic notation this is:
$exists space x,y space left( (space x ne y) land (space C(x) ne C(y)) right)$
or, without using $ne$, as follows:
$exists space x,y space left( lnot (space x = y) land lnot(space C(x) = C(y)) right)$
In fact, the qualification $x ne y$ is redundant, since $C(x) ne C(y) Rightarrow x ne y$. So we can simplify this to:
$exists space x,y space left(lnot(C(x) = C(y)) right)$
For the second part, if $B(x,y)$ denotes "$x$ is better than $y$" then "nobody is better than himself/herself" can be expressed as "there is no person $x$ such that $B(x,x)$". In formal logic notation this is:
$nexists space x space B(x,x)$
or
$forall space x space lnot B(x,x)$
answered Dec 10 '18 at 11:51
gandalf61gandalf61
8,481725
$endgroup$
$begingroup$
The answer is a bit misleading since you do not use boolean constants, but use colon and comma. This is at most just a suggestion how to write a correct formula, or an abbreviation of such. Yet not a formal logic notation.
$endgroup$
– Mad Hatter
Dec 10 '18 at 12:18
1
$begingroup$
@MadHatter I have changed the notation.
$endgroup$
– gandalf61
Dec 10 '18 at 13:50
add a comment |
$begingroup$
Suppose $C(x)$ denotes the colour $C$ of a car $x$. To translate "At least 2 cars are not the same colour" we could say "there are cars $x$ and $y$ that are not identical such that $C(x) ne C(y)$". In formal logic notation this is:
$exists space x,y space left( (space x ne y) land (space C(x) ne C(y)) right)$
or, without using $ne$, as follows:
$exists space x,y space left( lnot (space x = y) land lnot(space C(x) = C(y)) right)$
In fact, the qualification $x ne y$ is redundant, since $C(x) ne C(y) Rightarrow x ne y$. So we can simplify this to:
$exists space x,y space left(lnot(C(x) = C(y)) right)$
For the second part, if $B(x,y)$ denotes "$x$ is better than $y$" then "nobody is better than himself/herself" can be expressed as "there is no person $x$ such that $B(x,x)$". In formal logic notation this is:
$nexists space x space B(x,x)$
or
$forall space x space lnot B(x,x)$
answered Dec 10 '18 at 11:51
gandalf61gandalf61
8,481725
$endgroup$
$begingroup$
The answer is a bit misleading since you do not use boolean constants, but use colon and comma. This is at most just a suggestion how to write a correct formula, or an abbreviation of such. Yet not a formal logic notation.
$endgroup$
– Mad Hatter
Dec 10 '18 at 12:18
1
$begingroup$
@MadHatter I have changed the notation.
$endgroup$
– gandalf61
Dec 10 '18 at 13:50
add a comment |
$begingroup$
Suppose $C(x)$ denotes the colour $C$ of a car $x$. To translate "At least 2 cars are not the same colour" we could say "there are cars $x$ and $y$ that are not identical such that $C(x) ne C(y)$". In formal logic notation this is:
$exists space x,y space left( (space x ne y) land (space C(x) ne C(y)) right)$
or, without using $ne$, as follows:
$exists space x,y space left( lnot (space x = y) land lnot(space C(x) = C(y)) right)$
In fact, the qualification $x ne y$ is redundant, since $C(x) ne C(y) Rightarrow x ne y$. So we can simplify this to:
$exists space x,y space left(lnot(C(x) = C(y)) right)$
For the second part, if $B(x,y)$ denotes "$x$ is better than $y$" then "nobody is better than himself/herself" can be expressed as "there is no person $x$ such that $B(x,x)$". In formal logic notation this is:
$nexists space x space B(x,x)$
or
$forall space x space lnot B(x,x)$
answered Dec 10 '18 at 11:51
gandalf61gandalf61
8,481725
$endgroup$
Suppose $C(x)$ denotes the colour $C$ of a car $x$. To translate "At least 2 cars are not the same colour" we could say "there are cars $x$ and $y$ that are not identical such that $C(x) ne C(y)$". In formal logic notation this is:
$exists space x,y space left( (space x ne y) land (space C(x) ne C(y)) right)$
or, without using $ne$, as follows:
$exists space x,y space left( lnot (space x = y) land lnot(space C(x) = C(y)) right)$
In fact, the qualification $x ne y$ is redundant, since $C(x) ne C(y) Rightarrow x ne y$. So we can simplify this to:
$exists space x,y space left(lnot(C(x) = C(y)) right)$
For the second part, if $B(x,y)$ denotes "$x$ is better than $y$" then "nobody is better than himself/herself" can be expressed as "there is no person $x$ such that $B(x,x)$". In formal logic notation this is:
$nexists space x space B(x,x)$
or
$forall space x space lnot B(x,x)$
answered Dec 10 '18 at 11:51
gandalf61gandalf61
8,481725
edited Dec 10 '18 at 13:50
answered Dec 10 '18 at 11:51
gandalf61gandalf61
8,481725
answered Dec 10 '18 at 11:51
gandalf61gandalf61
8,481725
answered Dec 10 '18 at 11:51
gandalf61gandalf61
8,481725
8,481725
$begingroup$
The answer is a bit misleading since you do not use boolean constants, but use colon and comma. This is at most just a suggestion how to write a correct formula, or an abbreviation of such. Yet not a formal logic notation.
$endgroup$
– Mad Hatter
Dec 10 '18 at 12:18
1
$begingroup$
@MadHatter I have changed the notation.
$endgroup$
– gandalf61
Dec 10 '18 at 13:50
add a comment |
$begingroup$
The answer is a bit misleading since you do not use boolean constants, but use colon and comma. This is at most just a suggestion how to write a correct formula, or an abbreviation of such. Yet not a formal logic notation.
$endgroup$
– Mad Hatter
Dec 10 '18 at 12:18
1
$begingroup$
@MadHatter I have changed the notation.
$endgroup$
– gandalf61
Dec 10 '18 at 13:50
$begingroup$
The answer is a bit misleading since you do not use boolean constants, but use colon and comma. This is at most just a suggestion how to write a correct formula, or an abbreviation of such. Yet not a formal logic notation.
$endgroup$
– Mad Hatter
Dec 10 '18 at 12:18
$begingroup$
The answer is a bit misleading since you do not use boolean constants, but use colon and comma. This is at most just a suggestion how to write a correct formula, or an abbreviation of such. Yet not a formal logic notation.
$endgroup$
– Mad Hatter
Dec 10 '18 at 12:18
1
1
$begingroup$
@MadHatter I have changed the notation.
$endgroup$
– gandalf61
Dec 10 '18 at 13:50
$begingroup$
@MadHatter I have changed the notation.
$endgroup$
– gandalf61
Dec 10 '18 at 13:50
add a comment |
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