Mixing
Difference between these two logical expression
$begingroup$
I am trying to solve the following problem:
Let S(x) be the predicate “x is a student,” F(x) the predicate “x is a
faculty member,” and A(x, y) the predicate “x has asked y a question,”
where the domain consists of all people associated with your school.
Use quantifiers to express each of these statements. f ) Some student
has asked every faculty member a question.
What is the difference between
$forall y(F(y)toexists x(S(x)land A(x,y)))$
and $exists x (S(x) land forall y(F(y)to A(x,y)))$? A'int they same?
logic quantifiers
edited Aug 6 '15 at 13:09
lodrik
32717
asked Aug 6 '15 at 12:29
MystyMysty
234
$endgroup$
add a comment |
$begingroup$
I am trying to solve the following problem:
Let S(x) be the predicate “x is a student,” F(x) the predicate “x is a
faculty member,” and A(x, y) the predicate “x has asked y a question,”
where the domain consists of all people associated with your school.
Use quantifiers to express each of these statements. f ) Some student
has asked every faculty member a question.
What is the difference between
$forall y(F(y)toexists x(S(x)land A(x,y)))$
and $exists x (S(x) land forall y(F(y)to A(x,y)))$? A'int they same?
logic quantifiers
edited Aug 6 '15 at 13:09
lodrik
32717
asked Aug 6 '15 at 12:29
MystyMysty
234
$endgroup$
$begingroup$
Maybe you want to read this
$endgroup$
– Michael Galuza
Aug 6 '15 at 12:35
$begingroup$
For the first statement, did you mean $∀y(F(y)→∃x(S(x)∧A(x,y)))$?
$endgroup$
– Augustin
Aug 6 '15 at 12:39
add a comment |
$begingroup$
I am trying to solve the following problem:
Let S(x) be the predicate “x is a student,” F(x) the predicate “x is a
faculty member,” and A(x, y) the predicate “x has asked y a question,”
where the domain consists of all people associated with your school.
Use quantifiers to express each of these statements. f ) Some student
has asked every faculty member a question.
What is the difference between
$forall y(F(y)toexists x(S(x)land A(x,y)))$
and $exists x (S(x) land forall y(F(y)to A(x,y)))$? A'int they same?
logic quantifiers
edited Aug 6 '15 at 13:09
lodrik
32717
asked Aug 6 '15 at 12:29
MystyMysty
234
$endgroup$
I am trying to solve the following problem:
Let S(x) be the predicate “x is a student,” F(x) the predicate “x is a
faculty member,” and A(x, y) the predicate “x has asked y a question,”
where the domain consists of all people associated with your school.
Use quantifiers to express each of these statements. f ) Some student
has asked every faculty member a question.
What is the difference between
$forall y(F(y)toexists x(S(x)land A(x,y)))$
and $exists x (S(x) land forall y(F(y)to A(x,y)))$? A'int they same?
logic quantifiers
logic quantifiers
edited Aug 6 '15 at 13:09
lodrik
32717
asked Aug 6 '15 at 12:29
MystyMysty
234
edited Aug 6 '15 at 13:09
lodrik
32717
asked Aug 6 '15 at 12:29
MystyMysty
234
edited Aug 6 '15 at 13:09
lodrik
32717
edited Aug 6 '15 at 13:09
lodrik
32717
edited Aug 6 '15 at 13:09
lodrik
32717
32717
asked Aug 6 '15 at 12:29
MystyMysty
234
asked Aug 6 '15 at 12:29
MystyMysty
234
asked Aug 6 '15 at 12:29
MystyMysty
234
234
$begingroup$
Maybe you want to read this
$endgroup$
– Michael Galuza
Aug 6 '15 at 12:35
$begingroup$
For the first statement, did you mean $∀y(F(y)→∃x(S(x)∧A(x,y)))$?
$endgroup$
– Augustin
Aug 6 '15 at 12:39
add a comment |
$begingroup$
Maybe you want to read this
$endgroup$
– Michael Galuza
Aug 6 '15 at 12:35
$begingroup$
For the first statement, did you mean $∀y(F(y)→∃x(S(x)∧A(x,y)))$?
$endgroup$
– Augustin
Aug 6 '15 at 12:39
$begingroup$
Maybe you want to read this
$endgroup$
– Michael Galuza
Aug 6 '15 at 12:35
$begingroup$
Maybe you want to read this
$endgroup$
– Michael Galuza
Aug 6 '15 at 12:35
$begingroup$
For the first statement, did you mean $∀y(F(y)→∃x(S(x)∧A(x,y)))$?
$endgroup$
– Augustin
Aug 6 '15 at 12:39
$begingroup$
For the first statement, did you mean $∀y(F(y)→∃x(S(x)∧A(x,y)))$?
$endgroup$
– Augustin
Aug 6 '15 at 12:39
add a comment |
4 Answers
4
active
oldest
votes
$begingroup$
The first : Every faculty member was questioned by (at least) one student. The second : Some student asked every faculty member....
answered Aug 6 '15 at 14:59
DanielWainfleetDanielWainfleet
35.1k31648
$endgroup$
add a comment |
$begingroup$
Hint: Just read it out loud. The first says (simplified): "For every faculty member $y$, there is a student that asked $y$ a question". The second formula reads "There is a student that asked every faculty member a question".
answered Aug 6 '15 at 12:43
lodriklodrik
32717
$endgroup$
add a comment |
$begingroup$
In the first one you are saying: "For every faculty member, there exists a student...", whereas in the second one you are saying: "There is a student, and for all faculty members...". In this question we want the student to be fixed.
Also, the first one seems to actually read: "For all people y, if y is a faculty member then there exists a person x such that x is a student or x has asked y a question".
answered Aug 6 '15 at 12:43
SanteriSanteri
18817
$endgroup$
add a comment |
$begingroup$
The textbook answer says that the following represents:
Some student has asked every faculty member a question.
$forall y(F(y) to exists x (S(x) land A(x,y))) $
Which seems incorrect as I read this as saying for every faculty member there exists a student that has asked a question.
I'd argue that the following is more correct:
$exists x (S(x) land forall y (F(y) to A(x,y))) $
answered Jan 15 at 1:34
ElliottElliott
424
$endgroup$
add a comment |
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4 Answers
4
active
oldest
votes
4 Answers
4
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The first : Every faculty member was questioned by (at least) one student. The second : Some student asked every faculty member....
answered Aug 6 '15 at 14:59
DanielWainfleetDanielWainfleet
35.1k31648
$endgroup$
add a comment |
$begingroup$
The first : Every faculty member was questioned by (at least) one student. The second : Some student asked every faculty member....
answered Aug 6 '15 at 14:59
DanielWainfleetDanielWainfleet
35.1k31648
$endgroup$
add a comment |
$begingroup$
The first : Every faculty member was questioned by (at least) one student. The second : Some student asked every faculty member....
answered Aug 6 '15 at 14:59
DanielWainfleetDanielWainfleet
35.1k31648
$endgroup$
The first : Every faculty member was questioned by (at least) one student. The second : Some student asked every faculty member....
answered Aug 6 '15 at 14:59
DanielWainfleetDanielWainfleet
35.1k31648
answered Aug 6 '15 at 14:59
DanielWainfleetDanielWainfleet
35.1k31648
answered Aug 6 '15 at 14:59
DanielWainfleetDanielWainfleet
35.1k31648
answered Aug 6 '15 at 14:59
DanielWainfleetDanielWainfleet
35.1k31648
35.1k31648
add a comment |
add a comment |
$begingroup$
Hint: Just read it out loud. The first says (simplified): "For every faculty member $y$, there is a student that asked $y$ a question". The second formula reads "There is a student that asked every faculty member a question".
answered Aug 6 '15 at 12:43
lodriklodrik
32717
$endgroup$
add a comment |
$begingroup$
Hint: Just read it out loud. The first says (simplified): "For every faculty member $y$, there is a student that asked $y$ a question". The second formula reads "There is a student that asked every faculty member a question".
answered Aug 6 '15 at 12:43
lodriklodrik
32717
$endgroup$
add a comment |
$begingroup$
Hint: Just read it out loud. The first says (simplified): "For every faculty member $y$, there is a student that asked $y$ a question". The second formula reads "There is a student that asked every faculty member a question".
answered Aug 6 '15 at 12:43
lodriklodrik
32717
$endgroup$
Hint: Just read it out loud. The first says (simplified): "For every faculty member $y$, there is a student that asked $y$ a question". The second formula reads "There is a student that asked every faculty member a question".
answered Aug 6 '15 at 12:43
lodriklodrik
32717
answered Aug 6 '15 at 12:43
lodriklodrik
32717
answered Aug 6 '15 at 12:43
lodriklodrik
32717
answered Aug 6 '15 at 12:43
lodriklodrik
32717
32717
add a comment |
add a comment |
$begingroup$
In the first one you are saying: "For every faculty member, there exists a student...", whereas in the second one you are saying: "There is a student, and for all faculty members...". In this question we want the student to be fixed.
Also, the first one seems to actually read: "For all people y, if y is a faculty member then there exists a person x such that x is a student or x has asked y a question".
answered Aug 6 '15 at 12:43
SanteriSanteri
18817
$endgroup$
add a comment |
$begingroup$
In the first one you are saying: "For every faculty member, there exists a student...", whereas in the second one you are saying: "There is a student, and for all faculty members...". In this question we want the student to be fixed.
Also, the first one seems to actually read: "For all people y, if y is a faculty member then there exists a person x such that x is a student or x has asked y a question".
answered Aug 6 '15 at 12:43
SanteriSanteri
18817
$endgroup$
add a comment |
$begingroup$
In the first one you are saying: "For every faculty member, there exists a student...", whereas in the second one you are saying: "There is a student, and for all faculty members...". In this question we want the student to be fixed.
Also, the first one seems to actually read: "For all people y, if y is a faculty member then there exists a person x such that x is a student or x has asked y a question".
answered Aug 6 '15 at 12:43
SanteriSanteri
18817
$endgroup$
In the first one you are saying: "For every faculty member, there exists a student...", whereas in the second one you are saying: "There is a student, and for all faculty members...". In this question we want the student to be fixed.
Also, the first one seems to actually read: "For all people y, if y is a faculty member then there exists a person x such that x is a student or x has asked y a question".
answered Aug 6 '15 at 12:43
SanteriSanteri
18817
answered Aug 6 '15 at 12:43
SanteriSanteri
18817
answered Aug 6 '15 at 12:43
SanteriSanteri
18817
answered Aug 6 '15 at 12:43
SanteriSanteri
18817
18817
add a comment |
add a comment |
$begingroup$
The textbook answer says that the following represents:
Some student has asked every faculty member a question.
$forall y(F(y) to exists x (S(x) land A(x,y))) $
Which seems incorrect as I read this as saying for every faculty member there exists a student that has asked a question.
I'd argue that the following is more correct:
$exists x (S(x) land forall y (F(y) to A(x,y))) $
answered Jan 15 at 1:34
ElliottElliott
424
$endgroup$
add a comment |
$begingroup$
The textbook answer says that the following represents:
Some student has asked every faculty member a question.
$forall y(F(y) to exists x (S(x) land A(x,y))) $
Which seems incorrect as I read this as saying for every faculty member there exists a student that has asked a question.
I'd argue that the following is more correct:
$exists x (S(x) land forall y (F(y) to A(x,y))) $
answered Jan 15 at 1:34
ElliottElliott
424
$endgroup$
add a comment |
$begingroup$
The textbook answer says that the following represents:
Some student has asked every faculty member a question.
$forall y(F(y) to exists x (S(x) land A(x,y))) $
Which seems incorrect as I read this as saying for every faculty member there exists a student that has asked a question.
I'd argue that the following is more correct:
$exists x (S(x) land forall y (F(y) to A(x,y))) $
answered Jan 15 at 1:34
ElliottElliott
424
$endgroup$
The textbook answer says that the following represents:
Some student has asked every faculty member a question.
$forall y(F(y) to exists x (S(x) land A(x,y))) $
Which seems incorrect as I read this as saying for every faculty member there exists a student that has asked a question.
I'd argue that the following is more correct:
$exists x (S(x) land forall y (F(y) to A(x,y))) $
answered Jan 15 at 1:34
ElliottElliott
424
answered Jan 15 at 1:34
ElliottElliott
424
answered Jan 15 at 1:34
ElliottElliott
424
answered Jan 15 at 1:34
ElliottElliott
424
424
add a comment |
add a comment |
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$begingroup$
Maybe you want to read this
$endgroup$
– Michael Galuza
Aug 6 '15 at 12:35
$begingroup$
For the first statement, did you mean $∀y(F(y)→∃x(S(x)∧A(x,y)))$?
$endgroup$
– Augustin
Aug 6 '15 at 12:39