Translating a sentence into a predicate formulaExpress statements using symbolic logicWhat does 'any' mean in predicate calculusWould including the outside quantifier make more sense/be logically correct?Translating English to QuantifiersTranslating English to symbolic logicOrder of statements in implicationTranslating this nested quantifier to english (negation of nested quantifiers)How do I translate sentences from English to predicate logic?Nested Quantifiers (And vs Implies)Need someone to check if I am reading nested quantifiers correctly
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Translating a sentence into a predicate formula
Express statements using symbolic logicWhat does 'any' mean in predicate calculusWould including the outside quantifier make more sense/be logically correct?Translating English to QuantifiersTranslating English to symbolic logicOrder of statements in implicationTranslating this nested quantifier to english (negation of nested quantifiers)How do I translate sentences from English to predicate logic?Nested Quantifiers (And vs Implies)Need someone to check if I am reading nested quantifiers correctly
$begingroup$
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
44.8k103358
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
44.8k103358
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
44.8k103358
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
44.8k103358
asked Jan 23 at 16:16
Jinlin LIJinlin LI
1
edited Jan 23 at 16:25
N. F. Taussig
44.8k103358
asked Jan 23 at 16:16
Jinlin LIJinlin LI
1
edited Jan 23 at 16:25
N. F. Taussig
44.8k103358
edited Jan 23 at 16:25
N. F. Taussig
44.8k103358
edited Jan 23 at 16:25
N. F. Taussig
44.8k103358
44.8k103358
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 Mar 14 at 7:48
王文军 or Wenjun Wang王文军 or Wenjun Wang
514
$endgroup$
$begingroup$
@MauroALLEGRANZA Sir, may you check whether this solution is correct?
$endgroup$
– 王文军 or Wenjun Wang
Mar 14 at 7:59
add a comment |
Your Answer
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1 Answer
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1 Answer
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$begingroup$
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 Mar 14 at 7:48
王文军 or Wenjun Wang王文军 or Wenjun Wang
514
$endgroup$
$begingroup$
@MauroALLEGRANZA Sir, may you check whether this solution is correct?
$endgroup$
– 王文军 or Wenjun Wang
Mar 14 at 7:59
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 Mar 14 at 7:48
王文军 or Wenjun Wang王文军 or Wenjun Wang
514
$endgroup$
$begingroup$
@MauroALLEGRANZA Sir, may you check whether this solution is correct?
$endgroup$
– 王文军 or Wenjun Wang
Mar 14 at 7:59
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 Mar 14 at 7:48
王文军 or Wenjun Wang王文军 or Wenjun Wang
514
$endgroup$
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 Mar 14 at 7:48
王文军 or Wenjun Wang王文军 or Wenjun Wang
514
answered Mar 14 at 7:48
王文军 or Wenjun Wang王文军 or Wenjun Wang
514
answered Mar 14 at 7:48
王文军 or Wenjun Wang王文军 or Wenjun Wang
514
answered Mar 14 at 7:48
王文军 or Wenjun Wang王文军 or Wenjun Wang
514
514
$begingroup$
@MauroALLEGRANZA Sir, may you check whether this solution is correct?
$endgroup$
– 王文军 or Wenjun Wang
Mar 14 at 7:59
add a comment |
$begingroup$
@MauroALLEGRANZA Sir, may you check whether this solution is correct?
$endgroup$
– 王文军 or Wenjun Wang
Mar 14 at 7:59
$begingroup$
@MauroALLEGRANZA Sir, may you check whether this solution is correct?
$endgroup$
– 王文军 or Wenjun Wang
Mar 14 at 7:59
$begingroup$
@MauroALLEGRANZA Sir, may you check whether this solution is correct?
$endgroup$
– 王文军 or Wenjun Wang
Mar 14 at 7:59
add a comment |
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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