"Prove these logical equivalences, assuming that the domain is nonempty." "You will probably have to use a proof by cases on the two possible values of proposition" "∀yQ(y) and ∃yQ(y) respectively. This proof will use word arguments (not symbolic formula manipulation)." "(a) ∀x(∀yQ(y) → P (x)) ≡ ∀yQ(y) → ∀xP (x)"

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"Prove these logical equivalences, assuming that the domain is nonempty." "You will probably have to use a proof by cases on the two possible values of proposition" "∀yQ(y) and ∃yQ(y) respectively. This proof will use word arguments (not symbolic formula manipulation)." "(a) ∀x(∀yQ(y) → P (x)) ≡ ∀yQ(y) → ∀xP (x)"

Mathematics
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if i expand this out ... i get .. Ax~AyQ(y) v P(x) for the left and then for the right i get ~AyQ(y) v AxP(x) for the right
then i continue expanding out and get Ax ( Ey~Q(y) v P(x) ) on the left and on the right i get ... Ey~Q(y) v AxP(x)
and then im STUCK Lol ...

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Other answers:

i got confused
looks like ascii
its discrete math
Ah.
Well, I can help you, but I'm a bit rusty. Give me some time, lol.
ok lol sorry no can do but watch
thanks!!! ive been struggling for 3 hours or more
When you type A you mean it to be a universal quantification, and E is an existential one, right?
yes!
im not sure if i factored in properly but if you need to know any rules or confirm any rules i think i can confirm some of them ..
pikachu didnt i tell u if it has nothing to do with calc i skip?
Oh, my bad. Also, gah, discrete math. >.< I know basic proofs, but never had a formal class in it.
actually you know what .. you dont even have to factor it out ... you just have to look at it and then .. somehow prove that it can be equivalent .. i just notice on either side theres a EyQ(y)
3 in the morning is not the time to be asking actually high level math problems, lol.
its ok Lol .. ive been working on it all day .. im kinda stumped lol
ill figure it out somehow lol thanks anyway

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