Intro to Logic (prove sequents)

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    Intro Logic
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SUMMARY

This discussion focuses on proving specific logical sequents using formal logic techniques. The sequents presented include: 1) $(\exists x) Fx \to (\forall x) Gx \vdash (\exists x)(Fx \to (\forall x)Gx)$, 2) $(\forall x)(Fx \to (\forall y)\neg Fy) \vdash \neg(\exists x)Fx$, and 3) $(\exists x)Fx, (\forall x)(Fx \; à \; Gx) \vdash (\exists x)G$. Participants seek guidance on how to approach these proofs effectively.

PREREQUISITES
  • Understanding of first-order logic and quantifiers
  • Familiarity with sequent calculus
  • Knowledge of logical implications and their proofs
  • Experience with formal proof techniques
NEXT STEPS
  • Study the principles of sequent calculus in detail
  • Learn about the rules of quantifier manipulation in proofs
  • Explore examples of proving sequents in first-order logic
  • Practice constructing formal proofs for various logical statements
USEFUL FOR

Students of logic, mathematicians, and anyone interested in formal proof techniques in first-order logic will benefit from this discussion.

kk12
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I am stuck on these questions and don't really know how to start/solve them.
prove the following sequent:
1. $(\exists x) Fx \to (\forall x) Gx \vdash (\exists x)(Fx \to (\forall x)Gx)$

2. $(\forall x)(Fx \to (\forall y)\neg Fy) \vdash \neg(\exists x)Fx$

3. $(\exists x)Fx, (\forall x)(Fx \; à \; Gx) \vdash (\exists x)G$
 
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