Logic / Logic 265 · Atom · ~20 seconds

Quantifier Negation

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State

~(x)Fx :: (∃x)~Fx, and ~(∃x)Fx :: (x)~Fx.

Show

"Not everything is F" means something isn't. "Nothing is F" means everything isn't.

Watch for

Pushing ~ through a quantifier flips it. De Morgan's rules (204), one level down — same flip, same forgetting-hazard.