Statement to predicate formula
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
asked Nov 22 at 19:46
Ruben
246
add a comment |
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
asked Nov 22 at 19:46
Ruben
246
2
No; the second one means "Only worms are eaten by birds".
– Mauro ALLEGRANZA
Nov 22 at 19:50
add a comment |
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
asked Nov 22 at 19:46
Ruben
246
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
asked Nov 22 at 19:46
Ruben
246
asked Nov 22 at 19:46
Ruben
246
asked Nov 22 at 19:46
Ruben
246
asked Nov 22 at 19:46
Ruben
246
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
add a comment |
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
add a comment |
1 Answer
1
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.
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
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3009564%2fstatement-to-predicate-formula%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
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.
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
add a comment |
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.
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
add a comment |
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.
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.
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
add a comment |
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
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3009564%2fstatement-to-predicate-formula%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
2
No; the second one means "Only worms are eaten by birds".
– Mauro ALLEGRANZA
Nov 22 at 19:50