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Distributive properties of universal ąuantifier

Vx(p(x) Ag(x)) ć* Vxp(x)) A( Vxg{x)).

But:

Vx (p(x) Vg(x)) <K Vxp{x)) V( Vx g(x)). Example:jf

Vx(x 6 0 Vx >0) H. Vxx6 0) l/( Vx x>0)

. 1 to 1/0 Logic

Distributive Laws for quantiflers Distributive properties of existential ąuantifier

3x (p(x) Vg{x)) <=K3xp{x)) V{ 3x g(x)).

But:

3x (p(x) Ag(x)) =K3xp(x)) A{3xg(x)). Example:;t

3x (2\xA ~<2Ijc)) =>( 3x 2\x) A( 3x -<2Ijc))

.0 =łl Al Logic