MHB Conditional proof for multiple quantifier

Thread starter lize
Start date Mar 7, 2016
Tags

Conditional Multiple Proof

AI Thread Summary

To prove ((Ǝx) F(x) → (Ǝx) G(x)) using conditional proof, start with the premises: ((Ǝx) F(x) → (∀z) H(z)) and H(a) → G(b). The discussion suggests that a formal proof in logical calculus may be necessary for clarity. A reference link is provided for additional guidance on formal proofs. Understanding the relationship between existential and universal quantifiers is crucial in this context.

Mar 7, 2016

lize

Hi, I don't know how to prove ((Ǝx) F(x) →(Ǝx) (G(x)) with conditional proof from:
((Ǝx) F(x) → (∀z) H(z))
H(a) →G(b)

Thanks

Physics news on Phys.org

Mar 13, 2016

Evgeny.Makarov

Gold Member

MHB

What kind of proof do you have in mind? If you are talking about a formal proof in some logical calculus, then please see https://driven2services.com/staging/mh/index.php?threads/29/.

Thread 'Deductive proof in logic formal systems'

I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...

View full post »

Thread 'Onto set mapping is the surjective set mapping, and into injective?'

The textbook is being fine. I asked the forum for some introduction to topology, and decided to start with Simmon`s. This naive question is due to ignorance of the words into and onto, which I don't distinguish in Spanish. A quick browsing sugests I'm right.

View full post »