# Math Help - Logic question

1. ## Logic question

Hello

This is a logic question that appeared in one of the competitive exams that I am planning to give . I have no formal training in logic but I was reading about the traditional square of opposition online. I think this question can be done by traditional square of opposition but the statements are a bit complicated. They are not the simple "A" , "E" , " I" , "O" statements.

Can you please guide me on how to solve this question and if there is a proper way to solve them using some theorem which I dont know about?

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2. Let

$S\ =$ {solar systems in the Milky Way galaxy}
$P\ =$ {planets}
$M\ =$ {moons}

The astronomer’s assertion is

$(\forall\,x\in S)(\exists\,y\in P)$ $(y$ is in $x$ and $(\forall\,z\in M)(z$ revolves around $y\ \rightarrow\ z$ has life forms))

If you negate it, it becomes

$(\exists\,x\in S)(\forall\,y\in P)$ $(y$ is in $x\ \rightarrow\ (\exists\,z\in M)(z$ revolves around $y$ and $z$ has no life forms))

Can you translate that into non-mathematical English?

Spoiler:
There exists a solar system in the Milky Way galaxy such that for any planet in that solar system, there exists a moon which revolves around that planet and has no life forms.

3. using symbols really makes it easy! I am familiar with these symbols but not with operations of these symbols. for example: I did not know that negation of "there exists" becomes "for all" .

Can you please tell me what exact name is given to this field of logic? I want to search on internet for other similar practice exercises but dont know any good resource .

Any recommendations?

4. Originally Posted by champrock
Can you please tell me what exact name is given to this field of logic?
This branch of logic, involving quantifiers, is called the predicate calculus. (The other branch, not involving quantifiers, is called the propositional calculus.) Any good textbook on logic should contain a treatment of both propositional and predicate logic.