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Jan 25, 2012
equivalent to ¬P(x) v Q(x)
There is no x for which P(x)is true.
For all x, P(x) is false (¬P(x) is true)
There must be a counter example to P(x) (being true)
∃x∈D, P(x) is false
All employees earning over 110,000 are female.
Not all employees earning over 110,000 are female
There is an employee earning over 110,000 who is not female.
deﬁne O(x): ”x earns over 110,000”
∀x∈E, O(x) ⇒F(x) ←preferred statement
¬(∀x∈E, O(x) ⇒F(x)) ←equiv to. ∃x∈E, ¬(O(x) ⇒F(x))
(O(x) ⇒F(x)) is false when O(x) is True,
but F(x) is false. →O(x) ∧ ¬ F(x)
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