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How would I convert this discrete math statement from logic/equation to English?
What sort of math is this, and how would I solve it?How to logically analyze the statement: “Nobody in the calculus class is smarter than everybody in the discrete math class.”Converting to englishTranslating unless in logic to Englishfirst-order predicate calculusProve that all solutions to the equation x² = x +1 are irrationalHow do I translate sentences from English to predicate logic?Translations from English to Language of Predicate Logic (PL)Prove that the cardinality of the set of rational numbers and the set of integers is equalIf A, B, and C are Boolean variables, which of the following statements are true?
$begingroup$
Given that
$B(x)$ means "$x$ is a bear",
$F(x)$ means "$x$ is a fish", and
$E(x,y)$ means "$x$ eats $y$",
what is the best English translation of
$forall x[F(x)rightarrow forall y(E(y,x)rightarrow B(y))]$ ?
How can I do solve this? I got "Every fish is eaten by some bear", but that is not the answer. I'm not entirely sure how to go about this since I am fairly new to Discrete Math. Any help is greatly appreciated.
discrete-mathematics logic quantifiers logic-translation
edited Mar 29 at 6:04
Taroccoesbrocco
5,73671840
asked Mar 29 at 2:24
GrayGray
183
$endgroup$
add a comment |
$begingroup$
Given that
$B(x)$ means "$x$ is a bear",
$F(x)$ means "$x$ is a fish", and
$E(x,y)$ means "$x$ eats $y$",
what is the best English translation of
$forall x[F(x)rightarrow forall y(E(y,x)rightarrow B(y))]$ ?
How can I do solve this? I got "Every fish is eaten by some bear", but that is not the answer. I'm not entirely sure how to go about this since I am fairly new to Discrete Math. Any help is greatly appreciated.
discrete-mathematics logic quantifiers logic-translation
edited Mar 29 at 6:04
Taroccoesbrocco
5,73671840
asked Mar 29 at 2:24
GrayGray
183
$endgroup$
$begingroup$
“All predators of fish are bears” or “Every animal that eats fish must be a bear” are fair enough.
$endgroup$
– mjtsquared
Mar 29 at 2:36
$begingroup$
So how would you say "Every bear eats fish?"
$endgroup$
– mjw
Mar 29 at 3:26
$begingroup$
That’s not a correct simplification. Bears being the only animals that eat fish doesn’t always mean that all bears eat fish.
$endgroup$
– mjtsquared
Mar 29 at 4:36
add a comment |
$begingroup$
Given that
$B(x)$ means "$x$ is a bear",
$F(x)$ means "$x$ is a fish", and
$E(x,y)$ means "$x$ eats $y$",
what is the best English translation of
$forall x[F(x)rightarrow forall y(E(y,x)rightarrow B(y))]$ ?
How can I do solve this? I got "Every fish is eaten by some bear", but that is not the answer. I'm not entirely sure how to go about this since I am fairly new to Discrete Math. Any help is greatly appreciated.
discrete-mathematics logic quantifiers logic-translation
edited Mar 29 at 6:04
Taroccoesbrocco
5,73671840
asked Mar 29 at 2:24
GrayGray
183
$endgroup$
Given that
$B(x)$ means "$x$ is a bear",
$F(x)$ means "$x$ is a fish", and
$E(x,y)$ means "$x$ eats $y$",
what is the best English translation of
$forall x[F(x)rightarrow forall y(E(y,x)rightarrow B(y))]$ ?
How can I do solve this? I got "Every fish is eaten by some bear", but that is not the answer. I'm not entirely sure how to go about this since I am fairly new to Discrete Math. Any help is greatly appreciated.
discrete-mathematics logic quantifiers logic-translation
discrete-mathematics logic quantifiers logic-translation
edited Mar 29 at 6:04
Taroccoesbrocco
5,73671840
asked Mar 29 at 2:24
GrayGray
183
edited Mar 29 at 6:04
Taroccoesbrocco
5,73671840
asked Mar 29 at 2:24
GrayGray
183
edited Mar 29 at 6:04
Taroccoesbrocco
5,73671840
edited Mar 29 at 6:04
Taroccoesbrocco
5,73671840
edited Mar 29 at 6:04
Taroccoesbrocco
5,73671840
5,73671840
asked Mar 29 at 2:24
GrayGray
183
asked Mar 29 at 2:24
GrayGray
183
asked Mar 29 at 2:24
GrayGray
183
183
$begingroup$
“All predators of fish are bears” or “Every animal that eats fish must be a bear” are fair enough.
$endgroup$
– mjtsquared
Mar 29 at 2:36
$begingroup$
So how would you say "Every bear eats fish?"
$endgroup$
– mjw
Mar 29 at 3:26
$begingroup$
That’s not a correct simplification. Bears being the only animals that eat fish doesn’t always mean that all bears eat fish.
$endgroup$
– mjtsquared
Mar 29 at 4:36
add a comment |
$begingroup$
“All predators of fish are bears” or “Every animal that eats fish must be a bear” are fair enough.
$endgroup$
– mjtsquared
Mar 29 at 2:36
$begingroup$
So how would you say "Every bear eats fish?"
$endgroup$
– mjw
Mar 29 at 3:26
$begingroup$
That’s not a correct simplification. Bears being the only animals that eat fish doesn’t always mean that all bears eat fish.
$endgroup$
– mjtsquared
Mar 29 at 4:36
$begingroup$
“All predators of fish are bears” or “Every animal that eats fish must be a bear” are fair enough.
$endgroup$
– mjtsquared
Mar 29 at 2:36
$begingroup$
“All predators of fish are bears” or “Every animal that eats fish must be a bear” are fair enough.
$endgroup$
– mjtsquared
Mar 29 at 2:36
$begingroup$
So how would you say "Every bear eats fish?"
$endgroup$
– mjw
Mar 29 at 3:26
$begingroup$
So how would you say "Every bear eats fish?"
$endgroup$
– mjw
Mar 29 at 3:26
$begingroup$
That’s not a correct simplification. Bears being the only animals that eat fish doesn’t always mean that all bears eat fish.
$endgroup$
– mjtsquared
Mar 29 at 4:36
$begingroup$
That’s not a correct simplification. Bears being the only animals that eat fish doesn’t always mean that all bears eat fish.
$endgroup$
– mjtsquared
Mar 29 at 4:36
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
$forall x~(F(x)toforall y~(E(y,x)to B(y))$
$forall x~(xtext is a fishtoforall y~(ytext eats $x$to ytext is a bear))$
"If any fish is eaten by anything, then that thing is a bear."
Which I'd simplify to "Only bears eat fish."
answered Mar 29 at 2:59
Graham KempGraham Kemp
87.7k43578
$endgroup$
add a comment |
$begingroup$
It translates as : "For every fish, it is true that for anything that eats that fish, it is a bear". So ... this means that every fish only gets eaten by bears, i.e. That there is not anything that is not a bear that eats fish.
In short ... and colloquial English: Fish only get eaten by bears.
answered Mar 29 at 2:35
Bram28Bram28
64.2k44793
$endgroup$
2
$begingroup$
So, from the statements "Bears eat only fish", "Every bear eats fish", and "Only bears eat fish" the most correct would be: Only bears eat fish"?
$endgroup$
– Gray
Mar 29 at 2:41
$begingroup$
@Gray Actually, of those three, the latter one is the only correct one!
$endgroup$
– Bram28
Mar 29 at 13:51
add a comment |
Your Answer
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2 Answers
2
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oldest
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2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
$forall x~(F(x)toforall y~(E(y,x)to B(y))$
$forall x~(xtext is a fishtoforall y~(ytext eats $x$to ytext is a bear))$
"If any fish is eaten by anything, then that thing is a bear."
Which I'd simplify to "Only bears eat fish."
answered Mar 29 at 2:59
Graham KempGraham Kemp
87.7k43578
$endgroup$
add a comment |
$begingroup$
$forall x~(F(x)toforall y~(E(y,x)to B(y))$
$forall x~(xtext is a fishtoforall y~(ytext eats $x$to ytext is a bear))$
"If any fish is eaten by anything, then that thing is a bear."
Which I'd simplify to "Only bears eat fish."
answered Mar 29 at 2:59
Graham KempGraham Kemp
87.7k43578
$endgroup$
add a comment |
$begingroup$
$forall x~(F(x)toforall y~(E(y,x)to B(y))$
$forall x~(xtext is a fishtoforall y~(ytext eats $x$to ytext is a bear))$
"If any fish is eaten by anything, then that thing is a bear."
Which I'd simplify to "Only bears eat fish."
answered Mar 29 at 2:59
Graham KempGraham Kemp
87.7k43578
$endgroup$
$forall x~(F(x)toforall y~(E(y,x)to B(y))$
$forall x~(xtext is a fishtoforall y~(ytext eats $x$to ytext is a bear))$
"If any fish is eaten by anything, then that thing is a bear."
Which I'd simplify to "Only bears eat fish."
answered Mar 29 at 2:59
Graham KempGraham Kemp
87.7k43578
answered Mar 29 at 2:59
Graham KempGraham Kemp
87.7k43578
answered Mar 29 at 2:59
Graham KempGraham Kemp
87.7k43578
answered Mar 29 at 2:59
Graham KempGraham Kemp
87.7k43578
87.7k43578
add a comment |
add a comment |
$begingroup$
It translates as : "For every fish, it is true that for anything that eats that fish, it is a bear". So ... this means that every fish only gets eaten by bears, i.e. That there is not anything that is not a bear that eats fish.
In short ... and colloquial English: Fish only get eaten by bears.
answered Mar 29 at 2:35
Bram28Bram28
64.2k44793
$endgroup$
2
$begingroup$
So, from the statements "Bears eat only fish", "Every bear eats fish", and "Only bears eat fish" the most correct would be: Only bears eat fish"?
$endgroup$
– Gray
Mar 29 at 2:41
$begingroup$
@Gray Actually, of those three, the latter one is the only correct one!
$endgroup$
– Bram28
Mar 29 at 13:51
add a comment |
$begingroup$
It translates as : "For every fish, it is true that for anything that eats that fish, it is a bear". So ... this means that every fish only gets eaten by bears, i.e. That there is not anything that is not a bear that eats fish.
In short ... and colloquial English: Fish only get eaten by bears.
answered Mar 29 at 2:35
Bram28Bram28
64.2k44793
$endgroup$
2
$begingroup$
So, from the statements "Bears eat only fish", "Every bear eats fish", and "Only bears eat fish" the most correct would be: Only bears eat fish"?
$endgroup$
– Gray
Mar 29 at 2:41
$begingroup$
@Gray Actually, of those three, the latter one is the only correct one!
$endgroup$
– Bram28
Mar 29 at 13:51
add a comment |
$begingroup$
It translates as : "For every fish, it is true that for anything that eats that fish, it is a bear". So ... this means that every fish only gets eaten by bears, i.e. That there is not anything that is not a bear that eats fish.
In short ... and colloquial English: Fish only get eaten by bears.
answered Mar 29 at 2:35
Bram28Bram28
64.2k44793
$endgroup$
It translates as : "For every fish, it is true that for anything that eats that fish, it is a bear". So ... this means that every fish only gets eaten by bears, i.e. That there is not anything that is not a bear that eats fish.
In short ... and colloquial English: Fish only get eaten by bears.
answered Mar 29 at 2:35
Bram28Bram28
64.2k44793
answered Mar 29 at 2:35
Bram28Bram28
64.2k44793
answered Mar 29 at 2:35
Bram28Bram28
64.2k44793
answered Mar 29 at 2:35
Bram28Bram28
64.2k44793
64.2k44793
2
$begingroup$
So, from the statements "Bears eat only fish", "Every bear eats fish", and "Only bears eat fish" the most correct would be: Only bears eat fish"?
$endgroup$
– Gray
Mar 29 at 2:41
$begingroup$
@Gray Actually, of those three, the latter one is the only correct one!
$endgroup$
– Bram28
Mar 29 at 13:51
add a comment |
2
$begingroup$
So, from the statements "Bears eat only fish", "Every bear eats fish", and "Only bears eat fish" the most correct would be: Only bears eat fish"?
$endgroup$
– Gray
Mar 29 at 2:41
$begingroup$
@Gray Actually, of those three, the latter one is the only correct one!
$endgroup$
– Bram28
Mar 29 at 13:51
2
2
$begingroup$
So, from the statements "Bears eat only fish", "Every bear eats fish", and "Only bears eat fish" the most correct would be: Only bears eat fish"?
$endgroup$
– Gray
Mar 29 at 2:41
$begingroup$
So, from the statements "Bears eat only fish", "Every bear eats fish", and "Only bears eat fish" the most correct would be: Only bears eat fish"?
$endgroup$
– Gray
Mar 29 at 2:41
$begingroup$
@Gray Actually, of those three, the latter one is the only correct one!
$endgroup$
– Bram28
Mar 29 at 13:51
$begingroup$
@Gray Actually, of those three, the latter one is the only correct one!
$endgroup$
– Bram28
Mar 29 at 13:51
add a comment |
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$begingroup$
“All predators of fish are bears” or “Every animal that eats fish must be a bear” are fair enough.
$endgroup$
– mjtsquared
Mar 29 at 2:36
$begingroup$
So how would you say "Every bear eats fish?"
$endgroup$
– mjw
Mar 29 at 3:26
$begingroup$
That’s not a correct simplification. Bears being the only animals that eat fish doesn’t always mean that all bears eat fish.
$endgroup$
– mjtsquared
Mar 29 at 4:36