Observations About Quantifiers Flashcards
Æx p(x) => Ęx p(x)
Yes!
Only for non-empty Universe of Discourse
Ęx p(x) => Æx p(x)
No!
Does not logically imply
Ęx ( r(x) ^ s(x) ) = (Ęx r(x) ^ Ęx s(x) )
No!
Not logically equivalent
Ęx ( r(x) ^ s(x) ) => (Ęx r(x) ^ Ęx s(x) )
Yes!
It does logically imply
Æx p(x) = Ęx p(x)
No!
Not logically equivalent
Ęx ( p(x) v q(x) ) = ( Ęx p(x) v Ęx q(x) )
Yes!
It is logically equivalent
Æx ( p(x) ^ q(x) ) = (Æx p(x) ^ Æx q(x) )
Yes!
It is logically equivalent
Æx p(x) v Æx q(x) = Æx ( p(x) v q(x) )
No!
Not logically equivalent.
However, Æx p(x) v Æx q(x) => Æx ( p(x) v q(x) ). Just not the other way around.
Æx Æy p(x, y) = Æy Æx p(x, y)
Yes!
It is logically equivalent
Ęx Ęy p(x, y) = Ęy Ęx p(x, y)
Yes!
It is logically equivalent
Æx Ęy p(x, y) = Ęy Æx p(x, y)
No!
Not logically equivalent.
(Ęx r(x) ^ Ęx s(x) ) => Ęx ( r(x) ^ s(x) )
No!
It does not logically imply
