3
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3





0
P Q

x = y


3 3




"xP(x) x P(x)
"xP(x) x P(x)
x X = {x1, x2, . . . , xn} "xP(x) "xP(x)
P(x1) '" P(x2) '" . . . '" P(xn) P(x1) (" P(x2) (" . . . (" P(xn)


"!xP(x) Ô! ("xP(x)) '" ("x"y((P(x) '" P(y)) Ò! (x = y)))
"Q(x)P(x) Ô! "x(Q(x) '" P(x)) "Q(x)P(x) Ô! "x(Q(x) Ò! P(x))
"!xP(x) x P(x) "Q(x)P(x) "Q(x)P(x)
x Q(x) P(x) x Q(x) P(x)
3 3



(1) P n x1 x2 xn P(x1, x2, . . . ,
xn)
(2) Õ x (Õ) ŹÕ "xÕ "xÕ

(3) Õ È (Õ '" È) (Õ (" È) (Õ Ò! È) (Õ Ô! È)


Õ È Ć
x Õ x
Õ Õ "xÈ "xÈ
Õ
Õ "x "x . . . "x Õ x1 x2 xn Õ
1 2 n
Õ x1
y1 x2 y2 xn yn Õ(x1 := y1, x2 := y2, . . . , xn := yn)
3 3

Õ
Õ

Õ È
x È
("xÕ) Ò! Õ Õ Ò! ("xÕ)
(Ź"xÕ) Ô! ("xŹÕ) (Ź"xÕ) Ô! ("xŹÕ)
"x(Õ '" È) Ô! ("xÕ '" È) "x(Õ (" È) Ô! ("xÕ (" È)
"x(Õ '" È) Ô! ("xÕ '" È) "x(Õ (" È) Ô! ("xÕ (" È)
"x(Õ Ò! È) Ô! ("xÕ Ò! È) "x(È Ò! Õ) Ô! (È Ò! "xÕ)
"x(Õ Ò! È) Ô! ("xÕ Ò! È) "x(È Ò! Õ) Ô! (È Ò! "xÕ)
"xÕ Ô! "yÕ(x := y) "xÕ Ô! "yÕ(x := y) y Õ
"x"yÕ Ô! "y"xÕ "x"yÕ Ô! "y"xÕ "x"yÕ Ò! "y"xÕ



3 3

1

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"yQ(y) "x((P(x) '" ŹQ(x)) (" (ŹP(x) '" Q(x)))
"x((P(x) Ô! Q(x)) (" "yQ(y))
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