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We saw last time:
∀ -- a big ∧ over the entire domain
∃ -- a big ∨ over the entire domain
(On an empty domain, ∀ is always true and ∃ is always false.)
How to push ¬ over a quantifier
M(x): x is a minor
R(x): x is in this room
Older(x,y): x is older than y
multiple quantifiers
Somebody is older than Ian.
If you're older than Ian, you're not a minor.
Nobody is older than Ian.
Everybody is younger than Ian.
Everybody is younger than Ian except Ian himself.
aka
Ian is older than everybody else.
z is older than everybody else.
Somebody is older than everybody else.
Everybody is older than somebody.
∀x.∀y.Older(x,y)
∃x.∃y.Older(x,y)
∀x.∃y.Older(x,y)
∀x.∃y.Older(x,y)
Somebody is older than everybody else.
Everybody is older than somebody.
Every minor is younger than somebody in this class.
Some minor is younger than somebody in this class.
somebody in this room is older than every minor.
F(x,y,t): x fools y at time t.
Penny fools Ian today at 3pm.
Penny fools Ian all the time.
Vic fools somebody today at 3pm.
Vic can fool all of the people some of the time.
Vic can fool some of the people all of the time(*).
Vic can't fool all the people all of the time.
(replace with "vic" with "you"(meaning 'anybody'!))
(*) meaning: the *same* people are continually fooled -- English
is ambiguous -- hey, that's the whole reason we're using logic
instead of English!
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| ©2008, Ian Barland, Radford University Last modified 2008.Sep.19 (Fri) |
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