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Contradictory of (x) (y) (Axy -> By)?

 
 
Reply Thu 27 Feb, 2014 08:19 pm
Just as the title says. Whats the contradictory of (x) (y) (Axy -> By)? I'm guessing its something like ~(Ex) ~(Ey) ~(Axy & ~By).
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godcentral
 
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Reply Fri 28 Feb, 2014 10:58 pm
@godcentral,
It's ok someone already answered this at philosophy forums here:

http://forums.philosophyforums.com/threads/contradictory-of-x-y-axy-by-65457.html

If all sevens are after all sixes then all sixes are black.

It is false that if all sevens are after all sixes then all sixes are black.

So we just move the negation through the equation:

~(Vx) (Vy) (Axy -> By)

(3x)~ (Vy) (Axy -> By)
(3x)(3y) ~(Axy -> By)
(3x)(3y) ~(~Axy v By)
Now use De Morgan
(3x)(3y)(Axy & ~By)

Some sevens are after some sixes and it is false that some sixes are black.

I don't like the question because they mix a relation and a predicate.
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