Mixing
Translating a sentence into a predicate formula
$begingroup$
Problem 3.40. (a) Translate the following sentence into a predicate formula:
There is a student who has e-mailed at most n other people in the class,
besides possibly himself.
The domain of discourse should be the set of students in the class; in addition, the only predicates that you may use are
- equality,
- E.x; y/, meaning that “x has sent e-mail to y.”
(b) Explain how you would use your predicate formula (or some variant of it) to
express the following two sentences.
- There is a student who has emailed at least n other people in the class, besides possibly himself.
- There is a student who has emailed exactly n other people in the class, besides possibly himself.
discrete-mathematics
edited Jan 23 at 16:25
N. F. Taussig
44.7k103358
asked Jan 23 at 16:16
Jinlin LIJinlin LI
1
$endgroup$
add a comment |
$begingroup$
Problem 3.40. (a) Translate the following sentence into a predicate formula:
There is a student who has e-mailed at most n other people in the class,
besides possibly himself.
The domain of discourse should be the set of students in the class; in addition, the only predicates that you may use are
- equality,
- E.x; y/, meaning that “x has sent e-mail to y.”
(b) Explain how you would use your predicate formula (or some variant of it) to
express the following two sentences.
- There is a student who has emailed at least n other people in the class, besides possibly himself.
- There is a student who has emailed exactly n other people in the class, besides possibly himself.
discrete-mathematics
edited Jan 23 at 16:25
N. F. Taussig
44.7k103358
asked Jan 23 at 16:16
Jinlin LIJinlin LI
1
$endgroup$
1
$begingroup$
Do you know quantifiers ? Like e.g. $exists x$
$endgroup$
– Mauro ALLEGRANZA
Jan 23 at 16:18
$begingroup$
How are you asked to mange the "n" ? Do you know "numerical" quantifiers ? if not, Try with the simple cases : $n=1$ and $n=2$.
$endgroup$
– Mauro ALLEGRANZA
Jan 23 at 16:30
$begingroup$
How we have to read "besides possibly himself" ? That we have to exclude himself from counting, I think...
$endgroup$
– Mauro ALLEGRANZA
Jan 23 at 16:31
add a comment |
$begingroup$
Problem 3.40. (a) Translate the following sentence into a predicate formula:
There is a student who has e-mailed at most n other people in the class,
besides possibly himself.
The domain of discourse should be the set of students in the class; in addition, the only predicates that you may use are
- equality,
- E.x; y/, meaning that “x has sent e-mail to y.”
(b) Explain how you would use your predicate formula (or some variant of it) to
express the following two sentences.
- There is a student who has emailed at least n other people in the class, besides possibly himself.
- There is a student who has emailed exactly n other people in the class, besides possibly himself.
discrete-mathematics
edited Jan 23 at 16:25
N. F. Taussig
44.7k103358
asked Jan 23 at 16:16
Jinlin LIJinlin LI
1
$endgroup$
Problem 3.40. (a) Translate the following sentence into a predicate formula:
There is a student who has e-mailed at most n other people in the class,
besides possibly himself.
The domain of discourse should be the set of students in the class; in addition, the only predicates that you may use are
- equality,
- E.x; y/, meaning that “x has sent e-mail to y.”
(b) Explain how you would use your predicate formula (or some variant of it) to
express the following two sentences.
- There is a student who has emailed at least n other people in the class, besides possibly himself.
- There is a student who has emailed exactly n other people in the class, besides possibly himself.
discrete-mathematics
discrete-mathematics
edited Jan 23 at 16:25
N. F. Taussig
44.7k103358
asked Jan 23 at 16:16
Jinlin LIJinlin LI
1
edited Jan 23 at 16:25
N. F. Taussig
44.7k103358
asked Jan 23 at 16:16
Jinlin LIJinlin LI
1
edited Jan 23 at 16:25
N. F. Taussig
44.7k103358
edited Jan 23 at 16:25
N. F. Taussig
44.7k103358
edited Jan 23 at 16:25
N. F. Taussig
44.7k103358
44.7k103358
asked Jan 23 at 16:16
Jinlin LIJinlin LI
1
asked Jan 23 at 16:16
Jinlin LIJinlin LI
1
asked Jan 23 at 16:16
Jinlin LIJinlin LI
1
1
1
$begingroup$
Do you know quantifiers ? Like e.g. $exists x$
$endgroup$
– Mauro ALLEGRANZA
Jan 23 at 16:18
$begingroup$
How are you asked to mange the "n" ? Do you know "numerical" quantifiers ? if not, Try with the simple cases : $n=1$ and $n=2$.
$endgroup$
– Mauro ALLEGRANZA
Jan 23 at 16:30
$begingroup$
How we have to read "besides possibly himself" ? That we have to exclude himself from counting, I think...
$endgroup$
– Mauro ALLEGRANZA
Jan 23 at 16:31
add a comment |
1
$begingroup$
Do you know quantifiers ? Like e.g. $exists x$
$endgroup$
– Mauro ALLEGRANZA
Jan 23 at 16:18
$begingroup$
How are you asked to mange the "n" ? Do you know "numerical" quantifiers ? if not, Try with the simple cases : $n=1$ and $n=2$.
$endgroup$
– Mauro ALLEGRANZA
Jan 23 at 16:30
$begingroup$
How we have to read "besides possibly himself" ? That we have to exclude himself from counting, I think...
$endgroup$
– Mauro ALLEGRANZA
Jan 23 at 16:31
1
1
$begingroup$
Do you know quantifiers ? Like e.g. $exists x$
$endgroup$
– Mauro ALLEGRANZA
Jan 23 at 16:18
$begingroup$
Do you know quantifiers ? Like e.g. $exists x$
$endgroup$
– Mauro ALLEGRANZA
Jan 23 at 16:18
$begingroup$
How are you asked to mange the "n" ? Do you know "numerical" quantifiers ? if not, Try with the simple cases : $n=1$ and $n=2$.
$endgroup$
– Mauro ALLEGRANZA
Jan 23 at 16:30
$begingroup$
How are you asked to mange the "n" ? Do you know "numerical" quantifiers ? if not, Try with the simple cases : $n=1$ and $n=2$.
$endgroup$
– Mauro ALLEGRANZA
Jan 23 at 16:30
$begingroup$
How we have to read "besides possibly himself" ? That we have to exclude himself from counting, I think...
$endgroup$
– Mauro ALLEGRANZA
Jan 23 at 16:31
$begingroup$
How we have to read "besides possibly himself" ? That we have to exclude himself from counting, I think...
$endgroup$
– Mauro ALLEGRANZA
Jan 23 at 16:31
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Solution to part (a):
$
exists s Big((forall u ^neg E(s, u) ) land big( exists xexists y (xne y land y ne s land x ne s) land (E(s, x) lor E(s,y)) land forall z ((z ne x lor zne y lor z ne s) implies ^neg E(s,z))big) Big)
$
$(forall u ^neg E(s, u) )$ stands for the case that s does not send any one an email.
$ E(s, x) lor E(s,y)$ stands for 2 people
$forall z ((z ne x lor zne y lor z ne s) implies ^neg E(s,z))$ stands for at most 2 people
answered 7 hours ago
王文军 or Wenjun Wang王文军 or Wenjun Wang
484
$endgroup$
$begingroup$
@MauroALLEGRANZA Sir, may you check whether this solution is correct?
$endgroup$
– 王文军 or Wenjun Wang
6 hours ago
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',
autoActivateHeartbeat: false,
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%2f3084689%2ftranslating-a-sentence-into-a-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
$begingroup$
Solution to part (a):
$
exists s Big((forall u ^neg E(s, u) ) land big( exists xexists y (xne y land y ne s land x ne s) land (E(s, x) lor E(s,y)) land forall z ((z ne x lor zne y lor z ne s) implies ^neg E(s,z))big) Big)
$
$(forall u ^neg E(s, u) )$ stands for the case that s does not send any one an email.
$ E(s, x) lor E(s,y)$ stands for 2 people
$forall z ((z ne x lor zne y lor z ne s) implies ^neg E(s,z))$ stands for at most 2 people
answered 7 hours ago
王文军 or Wenjun Wang王文军 or Wenjun Wang
484
$endgroup$
$begingroup$
@MauroALLEGRANZA Sir, may you check whether this solution is correct?
$endgroup$
– 王文军 or Wenjun Wang
6 hours ago
add a comment |
$begingroup$
Solution to part (a):
$
exists s Big((forall u ^neg E(s, u) ) land big( exists xexists y (xne y land y ne s land x ne s) land (E(s, x) lor E(s,y)) land forall z ((z ne x lor zne y lor z ne s) implies ^neg E(s,z))big) Big)
$
$(forall u ^neg E(s, u) )$ stands for the case that s does not send any one an email.
$ E(s, x) lor E(s,y)$ stands for 2 people
$forall z ((z ne x lor zne y lor z ne s) implies ^neg E(s,z))$ stands for at most 2 people
answered 7 hours ago
王文军 or Wenjun Wang王文军 or Wenjun Wang
484
$endgroup$
$begingroup$
@MauroALLEGRANZA Sir, may you check whether this solution is correct?
$endgroup$
– 王文军 or Wenjun Wang
6 hours ago
add a comment |
$begingroup$
Solution to part (a):
$
exists s Big((forall u ^neg E(s, u) ) land big( exists xexists y (xne y land y ne s land x ne s) land (E(s, x) lor E(s,y)) land forall z ((z ne x lor zne y lor z ne s) implies ^neg E(s,z))big) Big)
$
$(forall u ^neg E(s, u) )$ stands for the case that s does not send any one an email.
$ E(s, x) lor E(s,y)$ stands for 2 people
$forall z ((z ne x lor zne y lor z ne s) implies ^neg E(s,z))$ stands for at most 2 people
answered 7 hours ago
王文军 or Wenjun Wang王文军 or Wenjun Wang
484
$endgroup$
Solution to part (a):
$
exists s Big((forall u ^neg E(s, u) ) land big( exists xexists y (xne y land y ne s land x ne s) land (E(s, x) lor E(s,y)) land forall z ((z ne x lor zne y lor z ne s) implies ^neg E(s,z))big) Big)
$
$(forall u ^neg E(s, u) )$ stands for the case that s does not send any one an email.
$ E(s, x) lor E(s,y)$ stands for 2 people
$forall z ((z ne x lor zne y lor z ne s) implies ^neg E(s,z))$ stands for at most 2 people
answered 7 hours ago
王文军 or Wenjun Wang王文军 or Wenjun Wang
484
answered 7 hours ago
王文军 or Wenjun Wang王文军 or Wenjun Wang
484
answered 7 hours ago
王文军 or Wenjun Wang王文军 or Wenjun Wang
484
answered 7 hours ago
王文军 or Wenjun Wang王文军 or Wenjun Wang
484
484
$begingroup$
@MauroALLEGRANZA Sir, may you check whether this solution is correct?
$endgroup$
– 王文军 or Wenjun Wang
6 hours ago
add a comment |
$begingroup$
@MauroALLEGRANZA Sir, may you check whether this solution is correct?
$endgroup$
– 王文军 or Wenjun Wang
6 hours ago
$begingroup$
@MauroALLEGRANZA Sir, may you check whether this solution is correct?
$endgroup$
– 王文军 or Wenjun Wang
6 hours ago
$begingroup$
@MauroALLEGRANZA Sir, may you check whether this solution is correct?
$endgroup$
– 王文军 or Wenjun Wang
6 hours ago
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.
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%2f3084689%2ftranslating-a-sentence-into-a-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
1
$begingroup$
Do you know quantifiers ? Like e.g. $exists x$
$endgroup$
– Mauro ALLEGRANZA
Jan 23 at 16:18
$begingroup$
How are you asked to mange the "n" ? Do you know "numerical" quantifiers ? if not, Try with the simple cases : $n=1$ and $n=2$.
$endgroup$
– Mauro ALLEGRANZA
Jan 23 at 16:30
$begingroup$
How we have to read "besides possibly himself" ? That we have to exclude himself from counting, I think...
$endgroup$
– Mauro ALLEGRANZA
Jan 23 at 16:31