Question with Predicate logic
$begingroup$
I have the question: "Translate the following argument into the language of predicate
logic. Determine if it is valid or invalid. Justify your answer by providing
either an interpretation or a proof.
All babies are illogical and nothing that is despised can manage
a crocodile. Not all illogical things are despised, therefore some
baby can manage some crocodile."
I have it translated in a way that I think is correct with
$$(∀x~(Bx → Ix) ∧ ∀y~(Mc → ¬Dy)) , \(∃x~(Ix → Dx))\
therefore~(∃x~(Bx → Mc))$$
I am trying to go through with a proof and I have not solved it, I keep on getting stuck while attempting it. Any help with forming a proof or an interpretation that proves it's validity would be greatly appreciated.
logic predicate-logic
edited Dec 5 '18 at 4:45
Graham Kemp
86.2k43478
asked Dec 5 '18 at 4:33
nintendoguy66nintendoguy66
1
$endgroup$
add a comment |
$begingroup$
I have the question: "Translate the following argument into the language of predicate
logic. Determine if it is valid or invalid. Justify your answer by providing
either an interpretation or a proof.
All babies are illogical and nothing that is despised can manage
a crocodile. Not all illogical things are despised, therefore some
baby can manage some crocodile."
I have it translated in a way that I think is correct with
$$(∀x~(Bx → Ix) ∧ ∀y~(Mc → ¬Dy)) , \(∃x~(Ix → Dx))\
therefore~(∃x~(Bx → Mc))$$
I am trying to go through with a proof and I have not solved it, I keep on getting stuck while attempting it. Any help with forming a proof or an interpretation that proves it's validity would be greatly appreciated.
logic predicate-logic
edited Dec 5 '18 at 4:45
Graham Kemp
86.2k43478
asked Dec 5 '18 at 4:33
nintendoguy66nintendoguy66
1
$endgroup$
1
$begingroup$
Your "translation" would be easier to follow if you explained what the predicate symbols stand for.
$endgroup$
– hardmath
Dec 5 '18 at 4:39
add a comment |
$begingroup$
I have the question: "Translate the following argument into the language of predicate
logic. Determine if it is valid or invalid. Justify your answer by providing
either an interpretation or a proof.
All babies are illogical and nothing that is despised can manage
a crocodile. Not all illogical things are despised, therefore some
baby can manage some crocodile."
I have it translated in a way that I think is correct with
$$(∀x~(Bx → Ix) ∧ ∀y~(Mc → ¬Dy)) , \(∃x~(Ix → Dx))\
therefore~(∃x~(Bx → Mc))$$
I am trying to go through with a proof and I have not solved it, I keep on getting stuck while attempting it. Any help with forming a proof or an interpretation that proves it's validity would be greatly appreciated.
logic predicate-logic
edited Dec 5 '18 at 4:45
Graham Kemp
86.2k43478
asked Dec 5 '18 at 4:33
nintendoguy66nintendoguy66
1
$endgroup$
I have the question: "Translate the following argument into the language of predicate
logic. Determine if it is valid or invalid. Justify your answer by providing
either an interpretation or a proof.
All babies are illogical and nothing that is despised can manage
a crocodile. Not all illogical things are despised, therefore some
baby can manage some crocodile."
I have it translated in a way that I think is correct with
$$(∀x~(Bx → Ix) ∧ ∀y~(Mc → ¬Dy)) , \(∃x~(Ix → Dx))\
therefore~(∃x~(Bx → Mc))$$
I am trying to go through with a proof and I have not solved it, I keep on getting stuck while attempting it. Any help with forming a proof or an interpretation that proves it's validity would be greatly appreciated.
logic predicate-logic
logic predicate-logic
edited Dec 5 '18 at 4:45
Graham Kemp
86.2k43478
asked Dec 5 '18 at 4:33
nintendoguy66nintendoguy66
1
edited Dec 5 '18 at 4:45
Graham Kemp
86.2k43478
asked Dec 5 '18 at 4:33
nintendoguy66nintendoguy66
1
edited Dec 5 '18 at 4:45
Graham Kemp
86.2k43478
edited Dec 5 '18 at 4:45
Graham Kemp
86.2k43478
edited Dec 5 '18 at 4:45
Graham Kemp
86.2k43478
86.2k43478
asked Dec 5 '18 at 4:33
nintendoguy66nintendoguy66
1
asked Dec 5 '18 at 4:33
nintendoguy66nintendoguy66
1
asked Dec 5 '18 at 4:33
nintendoguy66nintendoguy66
1
1
1
$begingroup$
Your "translation" would be easier to follow if you explained what the predicate symbols stand for.
$endgroup$
– hardmath
Dec 5 '18 at 4:39
add a comment |
1
$begingroup$
Your "translation" would be easier to follow if you explained what the predicate symbols stand for.
$endgroup$
– hardmath
Dec 5 '18 at 4:39
1
1
$begingroup$
Your "translation" would be easier to follow if you explained what the predicate symbols stand for.
$endgroup$
– hardmath
Dec 5 '18 at 4:39
$begingroup$
Your "translation" would be easier to follow if you explained what the predicate symbols stand for.
$endgroup$
– hardmath
Dec 5 '18 at 4:39
add a comment |
1 Answer
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$begingroup$
You want the second to say "There is an illogical thing and it is not despised."
Also the third should likewise say "There is a baby and it can manage crocodiles."
Remember, existential are restricted by a conjunction. Universals are restricted by a conditional.
answered Dec 5 '18 at 4:49
Graham KempGraham Kemp
86.2k43478
$endgroup$
add a comment |
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1 Answer
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1 Answer
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$begingroup$
You want the second to say "There is an illogical thing and it is not despised."
Also the third should likewise say "There is a baby and it can manage crocodiles."
Remember, existential are restricted by a conjunction. Universals are restricted by a conditional.
answered Dec 5 '18 at 4:49
Graham KempGraham Kemp
86.2k43478
$endgroup$
add a comment |
$begingroup$
You want the second to say "There is an illogical thing and it is not despised."
Also the third should likewise say "There is a baby and it can manage crocodiles."
Remember, existential are restricted by a conjunction. Universals are restricted by a conditional.
answered Dec 5 '18 at 4:49
Graham KempGraham Kemp
86.2k43478
$endgroup$
add a comment |
$begingroup$
You want the second to say "There is an illogical thing and it is not despised."
Also the third should likewise say "There is a baby and it can manage crocodiles."
Remember, existential are restricted by a conjunction. Universals are restricted by a conditional.
answered Dec 5 '18 at 4:49
Graham KempGraham Kemp
86.2k43478
$endgroup$
You want the second to say "There is an illogical thing and it is not despised."
Also the third should likewise say "There is a baby and it can manage crocodiles."
Remember, existential are restricted by a conjunction. Universals are restricted by a conditional.
answered Dec 5 '18 at 4:49
Graham KempGraham Kemp
86.2k43478
answered Dec 5 '18 at 4:49
Graham KempGraham Kemp
86.2k43478
answered Dec 5 '18 at 4:49
Graham KempGraham Kemp
86.2k43478
answered Dec 5 '18 at 4:49
Graham KempGraham Kemp
86.2k43478
86.2k43478
add a comment |
add a comment |
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$begingroup$
Your "translation" would be easier to follow if you explained what the predicate symbols stand for.
$endgroup$
– hardmath
Dec 5 '18 at 4:39