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CSC165H1 (200)
Lecture

jan25.pdf


Department
Computer Science
Course Code
CSC165H1
Professor
Tom Fairgrieve

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CSC165H1 Notes
Jan 25, 2012
retain:
P(x) Q(x)
equivalent to ¬P(x) v Q(x)
¬(xD, P(x))
xD, ¬P(x)
words;
There is no x for which P(x)is true.
equivalent to;
For all x, P(x) is false (¬P(x) is true)
when is
xD, P(x)
false?
There must be a counter example to P(x) (being true)
xD, P(x) is false
or
xD, ¬P(x)
¬(xD, P(x))
xD, ¬P(x)
Negate
All employees earning over 110,000 are female.
Not all employees earning over 110,000 are female
or
There is an employee earning over 110,000 who is not female.
define O(x): ”x earns over 110,000”
xO, F(x)
xE, O(x) F(x) preferred statement
¬(xE, O(x) F(x)) equiv to. xE, ¬(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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