Statement to predicate formula











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0
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Let B(x) mean “x is a bird”,



let W(x) mean “x is a worm”,



let E(x, y) mean “x eats y”.



There is a statement "Only birds eat worms".



If we translate this statement to predicate formula it will become:
$∀x∀y(W(x) ∧ E(y, x) → B(y))$



I was wondering will it be the same as $∀x∀y(B(x) ∧ E(x, y) → W(y))$ ?






logic predicate-logic quantifiers







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  • 2




    No; the second one means "Only worms are eaten by birds".
    – Mauro ALLEGRANZA
    Nov 22 at 19:50















up vote
0
down vote

favorite












Let B(x) mean “x is a bird”,



let W(x) mean “x is a worm”,



let E(x, y) mean “x eats y”.



There is a statement "Only birds eat worms".



If we translate this statement to predicate formula it will become:
$∀x∀y(W(x) ∧ E(y, x) → B(y))$



I was wondering will it be the same as $∀x∀y(B(x) ∧ E(x, y) → W(y))$ ?






logic predicate-logic quantifiers







share|cite|improve this question


















  • 2




    No; the second one means "Only worms are eaten by birds".
    – Mauro ALLEGRANZA
    Nov 22 at 19:50













up vote
0
down vote

favorite









up vote
0
down vote

favorite











Let B(x) mean “x is a bird”,



let W(x) mean “x is a worm”,



let E(x, y) mean “x eats y”.



There is a statement "Only birds eat worms".



If we translate this statement to predicate formula it will become:
$∀x∀y(W(x) ∧ E(y, x) → B(y))$



I was wondering will it be the same as $∀x∀y(B(x) ∧ E(x, y) → W(y))$ ?






logic predicate-logic quantifiers







share|cite|improve this question













Let B(x) mean “x is a bird”,



let W(x) mean “x is a worm”,



let E(x, y) mean “x eats y”.



There is a statement "Only birds eat worms".



If we translate this statement to predicate formula it will become:
$∀x∀y(W(x) ∧ E(y, x) → B(y))$



I was wondering will it be the same as $∀x∀y(B(x) ∧ E(x, y) → W(y))$ ?






logic predicate-logic quantifiers




logic predicate-logic quantifiers






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share|cite|improve this question











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asked Nov 22 at 19:46









Ruben

246




246








  • 2




    No; the second one means "Only worms are eaten by birds".
    – Mauro ALLEGRANZA
    Nov 22 at 19:50














  • 2




    No; the second one means "Only worms are eaten by birds".
    – Mauro ALLEGRANZA
    Nov 22 at 19:50








2




2




No; the second one means "Only worms are eaten by birds".
– Mauro ALLEGRANZA
Nov 22 at 19:50




No; the second one means "Only worms are eaten by birds".
– Mauro ALLEGRANZA
Nov 22 at 19:50










1 Answer
1






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votes

















up vote
1
down vote



accepted











If we translate this statement to predicate formula it will become:
$∀x∀y(W(x) ∧ E(y, x) → B(y))$




Anything will be a bird if it eats anything which is a worm.



Any eater of worms is a bird.



Only birds eat worms.




I was wondering will it be the same as $∀x∀y(B(x) ∧ E(x, y) → W(y))$ ?




Anything will be a worm if it is eaten by anything which is a bird.



Only worms are eaten by birds.






share|cite|improve this answer























  • Yeah, this does make sense. I thought that if only birds eat worms then it is the same as only worms are eaten by birds. Thanks for clarifying, your answer helped a lot!
    – Ruben
    Nov 23 at 0:05











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1 Answer
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active

oldest

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1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
1
down vote



accepted











If we translate this statement to predicate formula it will become:
$∀x∀y(W(x) ∧ E(y, x) → B(y))$




Anything will be a bird if it eats anything which is a worm.



Any eater of worms is a bird.



Only birds eat worms.




I was wondering will it be the same as $∀x∀y(B(x) ∧ E(x, y) → W(y))$ ?




Anything will be a worm if it is eaten by anything which is a bird.



Only worms are eaten by birds.






share|cite|improve this answer























  • Yeah, this does make sense. I thought that if only birds eat worms then it is the same as only worms are eaten by birds. Thanks for clarifying, your answer helped a lot!
    – Ruben
    Nov 23 at 0:05















up vote
1
down vote



accepted











If we translate this statement to predicate formula it will become:
$∀x∀y(W(x) ∧ E(y, x) → B(y))$




Anything will be a bird if it eats anything which is a worm.



Any eater of worms is a bird.



Only birds eat worms.




I was wondering will it be the same as $∀x∀y(B(x) ∧ E(x, y) → W(y))$ ?




Anything will be a worm if it is eaten by anything which is a bird.



Only worms are eaten by birds.






share|cite|improve this answer























  • Yeah, this does make sense. I thought that if only birds eat worms then it is the same as only worms are eaten by birds. Thanks for clarifying, your answer helped a lot!
    – Ruben
    Nov 23 at 0:05













up vote
1
down vote



accepted







up vote
1
down vote



accepted







If we translate this statement to predicate formula it will become:
$∀x∀y(W(x) ∧ E(y, x) → B(y))$




Anything will be a bird if it eats anything which is a worm.



Any eater of worms is a bird.



Only birds eat worms.




I was wondering will it be the same as $∀x∀y(B(x) ∧ E(x, y) → W(y))$ ?




Anything will be a worm if it is eaten by anything which is a bird.



Only worms are eaten by birds.






share|cite|improve this answer















If we translate this statement to predicate formula it will become:
$∀x∀y(W(x) ∧ E(y, x) → B(y))$




Anything will be a bird if it eats anything which is a worm.



Any eater of worms is a bird.



Only birds eat worms.




I was wondering will it be the same as $∀x∀y(B(x) ∧ E(x, y) → W(y))$ ?




Anything will be a worm if it is eaten by anything which is a bird.



Only worms are eaten by birds.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








answered Nov 22 at 23:17


























community wiki





Graham Kemp













  • Yeah, this does make sense. I thought that if only birds eat worms then it is the same as only worms are eaten by birds. Thanks for clarifying, your answer helped a lot!
    – Ruben
    Nov 23 at 0:05


















  • Yeah, this does make sense. I thought that if only birds eat worms then it is the same as only worms are eaten by birds. Thanks for clarifying, your answer helped a lot!
    – Ruben
    Nov 23 at 0:05
















Yeah, this does make sense. I thought that if only birds eat worms then it is the same as only worms are eaten by birds. Thanks for clarifying, your answer helped a lot!
– Ruben
Nov 23 at 0:05




Yeah, this does make sense. I thought that if only birds eat worms then it is the same as only worms are eaten by birds. Thanks for clarifying, your answer helped a lot!
– Ruben
Nov 23 at 0:05


















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