okey, thanks @A.P.

No problem

let's go

my first problem is

what is the meaning of each muslim is not privy to god

?

it means

all muslim or some muslims?

all muslims

option (2) is correct just in this case?

all?

What do you mean by "just"?

I means meaning of option (2) is all muslim is privy to god ?

Ok, let's try to make this clear (please excuse me if I'll be a bit pedantic).

afk

it's good that you pedantic

first inspect the meaning of option (2)

Ok, I'm back

okey

fist please clear meaning of (2).

Even before that, let's make clear if you understand what the sentence means

I think not all muslems is privy to god.

Here "privy" means (quoting from the dictionary) "made a participant in knowledge of something private or secret". So the sentence literally means "all Muslims do not know of God" (which is why I thought it to be extremely racist).

ok, so now please define meaning of )II)

To translate an English sentence into a logic sentence, basically you need to assign symbols to each part of the English sentence. Here (II) is: $\forall x(A(x) \to \neg B(x))$.

wait

I'm sure now, that the meaning of

main sentence is true.

is as follow

sorry

for arbitrary x, this is not true that x being Muslim and be privy to god.

$\forall x \neg (A(x) ^ B(x) $

that make (2) true.

First, there is no conjunction ("and") here, just an implication.

What you wrote would translate into $\forall x(\neg (A(x) \wedge B(x)))$, where $A(x)$ is "$x$ is a Muslim" and $B(x)$ is "$x$ is privy to God".

For ease of reference, let's call $S$ the original sentence, i.e. "each Muslim is not privy to God". Is it clear to you why this is the same as "for every person, if that person is a Muslim, then (s)he is not privy to God"?

$\forall x \neg [A(x) \wedge B(x)]$ is equivalent to $\forall x ( \neg A(x) \vee \neg B(x)) is equivalent to $\forall x (A(x) ---> \neg B(X)) ?!!!!!!!!!!!!!!!!!!!!!

Wait, it is true that $\neg A(x) \vee B(x)$ is equivalent to $A(x) \to B(x)$, but it doesn't come into the problem (there is no possible answer with a conjunction).

at last we have a implication not conjunction.

yes, that's the point

Anyway... Do you understand why $S$ is the same as "for every person, if that person is a Muslim, then (s)he is not privy to God"?

wait

i sent it

please see

You can use this to render math in the chat. Sorry, I thought you knew about that.

okey, what is wrong with my picture?

nothing !!!

I didn't say that. I just said that you can type math here instead of writing it on paper and posting a scanned image...

okey, please see my solution and say your idea ?

I also said that $\wedge$ (and $\vee$) are irrelevant for the problem at hand, because every available answer relies only on quantifiers, negations, and implications.

Now. Let's try to understand what (II) means:

okey

say

please

You can read $A(x) \to B(x)$ as "if $A(x)$ is true, then $B(x)$ is also true". The $\forall x$ in front of it means "the following formula holds for any $x$ you substitute into it".

okey so you means all x that muslem then not privy?

The point of the exercise is: can you define $A(x)$ and $B(x)$ in such a way that $\forall x(A(x) \to \neg B(x))$ has the same meaning as $S$?

more clearer please?

Yes, exactly. You get that meaning by defining $A(x)$ as "$x$ is Muslim" and $B(x)$ as "$x$ is privy to God".

okey I get it thanks

in 10 hours set bounty .

please remove chat history

So now you understand why (IV) is not a valid answer?

yes because atomic formula must be +

:)

Good.

thanks your are so kind

I don't think I can actively delete this chat room, but it should be deleted automatically after some time of inactivity, I think.

No problem.

thanks I say from your comment on below of your answer

Done. Please clean up your comments, too.