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5
5
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5
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5
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5

x
y x " y

x " y x y

u v w x y z t


10

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(1) x y x = y x " y

(2) Õ x (Õ) ŹÕ "xÕ "xÕ

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




x " y = y " x x " y = Ź(x " y) x = y = Ź(x = y)
/

x Ä…" y = "z(z " x Ò! z " y) x y = x Ä…" y '" x = y


x ‡" y = y Ä…" x x y = y x
x Ä…" y x y x y y x x y
x y y x
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""Ź(x " u)
u x


"
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u v

"" "(x " u Ô! x " v) Ô! u = v
u v x




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u v u

" "x " u Ò! " v " u '" "(x " v Ò! Ź(x " u))
u x v x


"

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Õ v
"""(x " v Ô! (x " u '" Õ))
u v x

u
Õ
u Õ

{x " u: Õ} u \ v = {x " u: x " v} u v
/
Õ
x " x x = x
/
v Õ
"u"v"x(x " v Ô! (x " u '" x " v))
/
"v"x(Õ Ò! x " v) {x " v: Õ}
{x: Õ}
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x y u x y
"""(x " u '" y " u)
x y u


{x, y} = {z: z = x (" z = y}

{x} = {x, x} x

(x, y) = {{x}, {x, y}}

(x, y) = (z, t) x = z y = t
{x, y} {x}



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x x " x
x x " x {x}


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u v u

"""(x " u Ò! x Ä…" v)
u v x


u u =


{x: "v"ux " v} u = {x: "v"ux " v}



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{x, y, z} = {{x}, {y, z}} {x, y, z, t} = {{x}, {y, z, t}}

(x, y, z) = ((x, y), z) (x, y, z, t) = ((x, y, z), t)

x *" y {x, y} x )" y {x, y} x *" y *" z {x, y, z} x )" y )" z

{x, y, z} {u} = {u} = u
u *" v = {x: x " u (" x " v} u )" v = {x: x " u '" x " v} u *" v *" w = {x:
x " u (" x " v (" x " w} u )" v )" w = {x: x " u '" x " v '" x " w}
u v u )" v = " u
x, y " u x )" y = " x = y

u ÷ v = (u \ v) *" (v \ u) u v
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u v u

"""(x Ä…" u Ò! x " v)
u v x
u
P(u) P(u) = {x: x Ä…" u}





x " u y " v (x, y) " P(P(u *" v)) u × v = {(x, y):
x " u '" y " v} u v
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" " " u '" "(x " u Ò! x *" {x} " u)
u x





S(u) = u *" {u} u
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Õ x y v


" " "!Õ Ò! " " " Õ
u x"u y v x"u y"v

u Õ
x y {y: "x"uÕ}


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u v
u

" " x = " '" " " (x = z Ò! x )" z = ") Ò! " " "x )" v = {z}

u x"u x"u z"u v x"u z




5 5