Question

I need help with discrete mathematics
Let P(x)
be the statement “Student x knows calculus” and
let Q(y)
be the statement “Class y contains a student who knows calculus.” Express each of these as quantification of P(x) and Q(y)
.
a) Some students know calculus.
b) Not every student knows calculus.
c) Every class has a student in it who knows calculus.
d) Every student in every class knows calculus.
e) There is at least one class with no students who know

Answer 1

i need help with c mostly

Answer 2

That so? What are your answers to a and b? ^_^

Answer 3

a)∃xP(x)

Answer 4

b)¬∀xP(x)

Answer 5

Okay, granted :>
Let's break c down...
Every class--> how do you represent this?

Answer 6

that where i get confused is the answer just ∀xQ(x) or it is more specific then that

Answer 7

Oh okay, so let's try reinterpreting that back into words, to allay your confusion ^_^

As per your definition, this adds up to:
For all classes x, Class x contains a student who knows calculus, yes?

Answer 8

ya

Answer 9

Is this not exactly what c is? :>

Answer 10

so the word has and contains are interchangeable

Answer 11

More or less, yes.
You have to use context ^_^

Answer 12

ok

Answer 13

No problem with d and e, then?

Answer 14

would d be ∀xP(x)and∀xQ(x)

Answer 15

is that right or no

Answer 16

Wait...

Answer 17

Okay, I'm not too sure about that, but if I must point something out, you might want to try a different variable for the ∀xQ(x), like y, for instance?

Answer 18

ok

Answer 19

ya i just typed that up to fast