, , . , , . . . , " ", " ".
: " a P " P (a); " S P " " x (S (x) P (x)) ( ); " S P " " x (S (x)Ø P (x)) ( ); " S P " $ x (S (x)Ù P (x)); ( ); " S P " $ x (A (x)ÙØ P (x)) ( ).
: ("), (), ($), (Ù).
2.3.
.
) .
" " " " P (x) = " x ". : P ().
) .
S (x) = " x "; P (x) = " x ". : " x (S (x) P (x)).
) .
S (x) = " x "; P (x) = " x ". : " x (S (x) Ø P (x)).
) .
S (x) = " x "; P (x) = " x ". : $ x (S (x) Ù P (x)).
) .
S (x) = " x "; P (x) = " x ". : $ x (A (x) Ù Ø P (x)).
. . .
2.4.
" " . , . .
: A (x) = " x "; B (y) = " y ", C (x, y) =
" x y ". " " :
|
|
|
$ x " y (A (x)Ù B (y) C (x, y)).
, :
Ø$ x " y (A (x)Ù B (y) C (x, y))) º " x $ y (Ø(A (x)Ù B (y) C (x, y))º
º " x $ y (A (x)Ù B (y)Ù Ø C (x, y)).
:
" ".
1. .
2. . , . .
1
1. " x (P (x)Ù R (x)$ yQ (x,y)).
2. .
2
1. " x (P (x)(R (x)((yQ (x,y)).
2. .
3
1. " xP (x)$ yP (y))Ú" z $x R (x, z).
2. , 2, .
4
1. " x ($ y (Ø P (x)Ù Q (y)) R (y, z)).
2. .
5
1. " x ($ y (Ø P (x, y)Ù Q (y, z))).
2. .
6
1. " x ($ y (Ø P (x))Ù Q (y)).
2. .
7
1. " x ($ y (Ø P (x))Q (y, z)).
2. .
8
1. " x (P (x) Q (x, y)) ($yP(y) $ z Q(y, z)).
2. .
9
1. $ x P(x, y) (Q (x) Ø$ u (P (x, u))).
2. .
10
1. " x " y ($ zP (x, z) Ù Q (x, z)) $ uR (x, y, u).
2. .
11
1. " x (P (x) $ y (Q (x, y) Ú $ zR (x, y, z))).
2. .
12
1. " x (P (x) $ yQ (x, y).
2. .
13
1. Ø($ x " yP (x, y)Ú (" x " y $ zQ (x, y, z)))Ù$ yR (y).
2. .
14
1. " x (P (x) Ø($ y " zQ (x, y, z))).
2. .
15
1. ((Ø$ xP (x)) Ú (" xQ (x))Ù(R (x) " yS (x, y)).
2. .
16
1." x P (x) $ xQ (x).
2. .
17
1. (Ø" xP (x) Ú $ xQ (x))Ù(R $ S (x, y)).
2. .
18
1. P (x, y) Ø($ xQ (x, y)Ú" uP (u)).
2. .
19
1. " x " y (Q (x) Ø(P (x, y)ÚØ($ uR (x, y, u)))).
2. .
|
|
|
20
1. Ø P (x, y) (" xQ (x)ÙØ($ y " uR (y, u, y))).
2. .
