Two place predicate logic

Question

How to solve these type of question:-

∀x ∀y (x+y = 0)

∀x ∃y (x+y = 0)

∃x ∀y (x+y = 0)

∃x ∃y (x+y = 0)

??

Comments

You should refer Rosen first chapter.Solve exercise problems.

Answer 1

Quantifiers in series could be seen as nested loops

∀x ∀ y could be seen as :

for every x

{

   for every y

     {

          logical function(x,y)

     }

}

whereas ∃ y could be seen as an assignment in programming

so ∀x ∃ y could be implemented as :

for every x

{

  y=y₁

 logical function(x,y)
}

And like this you can try all possible combinations.