=

#A A


A *" B : = {x: x " A (" x " B}

A )" B : = {x: x " A '" x " B}

A \ B : = {x: x " A '" <" x " B}

A X A : = {x: x " X'" <" x " A}

P(A): = {D : D ‚" A}


A *" A = A A )" A = A
A *" B = B *" A A )" B = B )" A
A *" (A )" B) = A A )" (A *" B) = A
A *" (B )" C) = (A *" B) )" (A *" C) A )" (B *" C) = (A )" B) *" (A )" C)
A *" " = A A )" " = "
(A *" B) = A )" B (A )" B) = A *" B
(A ) = A (") = X
A ‚" B =Ò! B ‚" A

n

A1 *" A2 *" · · · *" An : = Ai
i=1
n

A1 )" A2 )" · · · )" An : = Ai
i=1
"

A1 *" A2 *" A3 *" . . . = Ai : = x: " x " Ai
i"N
i=1
"

A1 )" A2 )" A3 )" . . . = Ai : = x: " x " Ai
i"N
i=1




( Ai) = A i ( Ai) = A i
i"I i"I i"I i"I
(Ai *" Bi) = Ai *" Bi (Ai )" Bi) = Ai )" Bi
i"I i"I i"I i"I i"I i"I
(Ai )" Bi) ‚" Ai )" Bi (Ai *" Bi) ƒ" Ai *" Bi
i"I i"I i"I i"I i"I i"I
A *" ( Ai) = (A *" Ai) A )" ( Ai) = (A )" Ai)
i"I i"I i"I i"I
A *" ( Ai) = (A *" Ai) A )" ( Ai) = (A )" Ai)
i"I i"I i"I i"I
Ai \ Bi ‚" (Ai \ Bi) Ai \ Bi ƒ" (Ai \ Bi)
i"I i"I i"I i"I i"I i"I


A × B : = {(a, b): a " A, b " B}

A × (B *" C) = (A × B) *" (A × C)
A × (B )" C) = (A × B) )" (A × C)
A × (B \ C) = (A × B) \ (A × C)
A × B = B × A Ð!Ò! A = B
(X × Y ) \ (A × B) = [(X \ A) × Y ] *" [X × (Y \ B)]










A = {1, 2, 3} B = {c&, `&, } C = {"}



A B A B A *" B A )" B A \ B B \ A





3x-1
0.5
A = x: e" 4 B = x: 3log (x2-5x+7) < 1
5-x
"
3 2
x
4
A = x: x < ( x)x -x+1 B = x: logx-3 x-2 e" 1
x-4




I = {1, 2, 3} A1 = {a, b, c, d} A2 = {c, d, e, f} A3 = {a, c, f, g}

Ai Ai
i"I i"I






1 1
Ai = 2 - , 3 + , i " N
i i


Ai = {x " R: x = sin i} , i " R

K(A, r) A = (x, 0) r > 0


K(A, r), K(A, r),
r"R+ r"R+
K(A, r), K(A, r).
x"R x"R




A × B B × A


A = {-1, 2, 3} B = 0, 2)


A = {x " R: |x - 3| d" 2} B = {y : |y| e" 3}


A = {x " R: sin x e" cos x} B = {y : y " R}


" "

1 n+1
A = -n, B = Bn, Bn = {x " R: x2 + n - 2 = 0}
n
n=1 n=1



A × (B \ C) = (A × B) \ (A × C)