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Which one of the following is NOT logically equivalent to $¬∃x(∀ y (α)∧∀z(β ))$ ?

1. $∀ x(∃ z(¬β )→∀ y(α))$
2. $∀x(∀ z(β )→∃ y(¬α))$
3. $∀x(∀ y(α)→∃z(¬β ))$
4. $∀x(∃ y(¬α)→∃z(¬β ))$

1 comment

It's simply based on Demorgan's law

$\sim \exists x(\forall y(\alpha )\wedge \forall z(\beta ))$

∃x(∀z(β)∨∀y(α)) as  ∃x(∀y(α)∨∀z(β)) ?

→ Yes we can write that way. @ankitrazzagmail.com

→ Option D should be as per commented by @Tesla!

D.∀x(∃y(¬α)→∃z(β))

its ∃z (¬β) in D  option.

option A

by

Thanks a lotss ..Sir
Good method of solving through variables p and q.