Thread: express using quatifiers

I'm not entirely sure if this is posted in the right place so i'm sorry if its not.



Let the predicates M, T and C be defined by
M(x, y) means x has sent y an email message
T (x, y) means x has telephoned y
C(x) means x is a student


Express each of the following using quantifiers

a) No student has telephoned John
b) Some students have been sent an email by Graham.
c) There are two students who have telephoned one another
d) There is at least one student who has either telephoned or emailed every other student
student.
e) Every student has either been sent an email message or had a telephone call from some other student.


Ok so I have tried to do this but I have no idea if I'm right.

(¬ means 'not', A means 'For All' E means 'There exists')
for part a I get something like this

T(¬EC(x),John)

but my friend got

¬Ex, C(x) ^ (y = John => T(x,y))

not sure im doing this right?

Hello djmccabie

Originally Posted by djmccabie

I'm not entirely sure if this is posted in the right place so i'm sorry if its not.



Let the predicates M, T and C be defined by
M(x, y) means x has sent y an email message
T (x, y) means x has telephoned y
C(x) means x is a student


Express each of the following using quantifiers

a) No student has telephoned John
b) Some students have been sent an email by Graham.
c) There are two students who have telephoned one another
d) There is at least one student who has either telephoned or emailed every other student
student.
e) Every student has either been sent an email message or had a telephone call from some other student.


Ok so I have tried to do this but I have no idea if I'm right.

(¬ means 'not', A means 'For All' E means 'There exists')
for part a I get something like this

T(¬EC(x),John)

but my friend got

¬Ex, C(x) ^ (y = John => T(x,y))

not sure im doing this right?

Your friend is nearer the answer than you. I should write (a) as

(b) Re-write this as: There exists an such that is a student, and Graham has sent an email. So

(c) Re-write as: There exists an , there exists a such that is a student and is a student and has telephoned and has telephoned . So

. Can you complete?

(d) Re-write as: There exists an such that for all , is a student and if is a student then ( has telephoned or has emailed ). Can you complete?

(e) For all , there exists a such that is a student and if is a student then ( has emailed or has telephoned ). Can you complete?

Grandad

Originally Posted by djmccabie

I'm not entirely sure if this is posted in the right place so i'm sorry if its not.



Let the predicates M, T and C be defined by
M(x, y) means x has sent y an email message
T (x, y) means x has telephoned y
C(x) means x is a student


Express each of the following using quantifiers

a) No student has telephoned John
b) Some students have been sent an email by Graham.
c) There are two students who have telephoned one another
d) There is at least one student who has either telephoned or emailed every other student
student.
e) Every student has either been sent an email message or had a telephone call from some other student.


Ok so I have tried to do this but I have no idea if I'm right.

(¬ means 'not', A means 'For All' E means 'There exists')
for part a I get something like this

T(¬EC(x),John)

but my friend got

¬Ex, C(x) ^ (y = John => T(x,y))

not sure im doing this right?

Your friend is right: you cannot quantify inside the predicate T

Tonio