Thread: Quantifiers and Predicates--Due tomorrow at (9:00) Need Help

1. Quantifiers and Predicates--Due tomorrow at (9:00) Need Help

I am so lost and dont understand this question?

Q: Use quantifiers and predicates with more than one variable to express these statements.

a.) There is a student in this class who can speak Hindu.
b.) Every Student in this class plays some sport.
c.) Some student in this class have visited Alaska but have not visited Hawaii.
d.) All students in this class have learned at least one programming language.
e.) There is a student in this class who has taken every course offered by one of the
departments in this school.
f.) Some student in this class grew up in the same town as exactly one other student in this
class.
g.) Every student in this class has chatted with one other student in at least one chat group.

2. Below is my attempt: (I can't guarantee that it is 100% correct.)

a) There is a student in this class who can speak Hindu.
$\exists x$(Student(x) $\wedge$ Speaks(x, Hindu))

b) Every Student in this class plays some sport.
$\forall x$(Student(x) $\rightarrow \exists$y(Play(x,y) $\wedge$Sport(y)))

c)Some student in this class have visited Alaska but have not visited Hawaii.
$\exists x$(Student(x) $\wedge$Visited(x, Alaska) $\wedge \neg$Visited(x, Hawaii))

d)All students in this class have learned at least one programming language.
$\forall x$(Student(x) $\rightarrow \exists$y(Learned(x,y) $\wedge$ProgLanguage(y)))

e)There is a student in this class who has taken every course offered by one of the departments in this school.
$\exists x$(Student(x) $\wedge \forall y \exists z$((Taken(x,y) $\wedge$Course(y)) $\rightarrow$(OfferedBy(y,z) $\wedge$Department(z))))

f)Some students in this class grew up in the same town as exactly one other student in this class.
$\exists x \exists y \exists z$(Student(x) $\wedge$Student(z) $\wedge$Grewup(x,y)) $\wedge$Grewup(z,y) $\wedge$Town(y)) $\wedge$ $(x \neg = z))$

g)Every student in this class has chatted with one other student in at least one chat group.
$\forall x \exists y \exists z$((Student(x) $\wedge$Chatted(x,y) $\wedge$MemberOf(x,z) $\wedge$Chatgroup(z)) $\rightarrow$ $\forall k ((y \neg = k) \rightarrow \neg$Chatted(x,k))))

3. Quantifiers and Predicates

Hello Grillakis

This help may come too late - if so, try to post your questions a bit earlier next time!

In each case define the Universe of Discourse as {Students in this class}. The question asks for predicates with more than one variable. So we define them in the form P(x, y), which means 'x has property y'. For instance, we could define loves(x, y) to mean 'x loves y'. Then:
Originally Posted by Grillakis
a.) There is a student in this class who can speak Hindu.
Define speaks(x, y) as 'x can speak language y'

Then $\exists$ x, speaks(x, Hindu)

Originally Posted by Grillakis
b.) Every Student in this class plays some sport.
Define plays(x, y) as 'x plays sport y'

Then $\forall$ x, $\exists$ y, plays(x, y)

Originally Posted by Grillakis
c.) Some student in this class have visited Alaska but have not visited Hawaii.
Define visited(x, y) as 'x has visited y'

Then $\exists$ x, visited(x, Alaska) $\wedge\neg$visited(x, Hawaii)
Originally Posted by Grillakis
d.) All students in this class have learned at least one programming language.
Define learned(x, y) as 'x has learned programming language y'

Then $\forall$ x, $\exists$ y, learned(x, y)
Originally Posted by Grillakis
e.) There is a student in this class who has taken every course offered by one of the departments in this school.
Define takenCourse(x, y, z) as 'x has taken course y, offered by department z in this school'

Then $\exists$ x, z, $\forall$ y takenCourse(x, y, z)
Originally Posted by Grillakis
f.) Some student in this class grew up in the same town as exactly one other student in this class.
Define sameTown(x, y) as 'x grew up in the same town as y'

Then $\exists$ x, y, sameTown(x, y) $\wedge$ (sameTown(x, z) $\Rightarrow$ z = y)
Originally Posted by Grillakis
g.) Every student in this class has chatted with one other student in at least one chat group.
Define chatted(x, y, z) as 'x has chatted with y in chat group z'

Then $\forall$ x, $\exists$ y, z, chatted(x, y, z)

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there is a student in this class who can speak hindi

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