Elements of mathematical logic

[Victoria124]

How i solve this :"For every binary predicate p(x,y),it's asked to verify that the sentence : (∃x)(∀y)p(x,y)→(∀y)(∃x)p(x,y) is true." ?

 

[pka]

How i solve this :"For every binary predicate p(x,y),it's asked to verify that the sentence : (∃x)(∀y)p(x,y)→(∀y)(∃x)p(x,y) is true." ?

The problem with trying to help with these is that every author and/or textbook use different notation or rules.
This one goes something like:
\(\displaystyle (\exists x)(\forall y)P(x,y)~~P\\(\forall y)P(t,y)~~E.I.\\P(t,u)~~U.I.\\(\exists x)P(x,u)~~E.G.\\(\forall y)(\exists x) P(x,y)~~U.G.\).

BUT, you must check your text/notes for the correct rules of inference.

 

[Victoria124]

Thank you very much,but can you tell me what do E.I. and U.I mean?

 

[pka]

Thank you very much,but can you tell me what do E.I. and U.I mean?

E.I. Existential Instantiation
U.I. Universal Instantiation

E.G. Existential Generalization
U.G. Universal Generalization