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1. 1. 2 14 (30 )
2. 1 ! " # 10 10
2 ! # 4 20
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1. $ P(A) ! ' ( P(B) *+# A , B ! ' -+. , n(X) ! 123 ( ' X
, A , B 4 563 #7 (8"
3. A ! ' ( B . B ! ' ( A
. A = B (. n(A) = n(B)
2. 3 : + ' +( 7 8
A = {x R | x2
- 2x + 1 = 0} B = {x R | x2
- 3x + 2 = 0}
C = { x R | x2
- 5x + 6 = 0}
( 52 # 4 56 ( 7, '
3. A B C . A B C . A B C (. A B C
3. 3 : +-: ' A, B, C ! ' -+. , 8 7-17 ' 6 $ A B , B C , 123
( ' -+ 7 3 F+
3. A B C . A B . A C (. B C
4. $ A ! ' ( 3 " x4
- 4x3
- x2
+ 16x - 12 = 0, B = {1, 2, 3} (: 7 ' A , B
4 563 #7 (8"
3. A B . B A . A B = A (. A B = B
5. -+$G3 ( H A , B ! ' -+.
3. A B = {} 3I 7 H A B . A (B C) = (A B) ( A C)
. A J B = {x | x A , x B} (. A B = {x | x A , x B}
6. 2# 3 "+ 2 3 " +( 7 8
A B = (A B ) J (B A )
*+# U ! ' ( 3K4 4 56, A, B, C ! ' -+. 8 7 ! ' 7 ( , 8 7 7 -+"7 3
, n(X) H 123 ( ' X
(42 "L 7 -+ 7 8 3,7 $G3 (
3. A B = B A . (A B) C = A (B C)
. n(A B) = n(B A) (. 8 7 -+3,7 $G3 (

2. 7. 2# 3 "+ 2 3 " +(
A B = {x J y | x A, y B , x > y}
H A = {J2, J1, 0, 1, 2, 3}, B = {J1, 0, 1, 2, 3} -+ 7 8 3,7 $G3 (
3. A B {x | x5
J 6x4
+ 12x3
J 12x2
+ 11x J 6 = 0}
. (A B) A (A B) B
. (A B) J B = (A B) J A
(. 3,7 $G3 ( F3
8. 2# 3 "+ 2 3 " P+Q +( 7 8
A + B = {x + y | x A, y B , x + y 0}
3 : +-: A = {J1, 0, 1}, B = {0, 1, 2}, C = {0, 1} , n(X) H 123 ( ' X -+ 7 8
3,7 $G3 (
3. n(A + B) = n(A) + n(B)
. n[(A + B) + C] = n(A) + n(B) + n(C)
. ' (: + ( ' A + B 7 3 16
(. $G3 F3
9. ' ,I3 F+ ( ' (A J B ) (C J D ) (E J F ) X (Y J Z ) *+# A B C
D X Y Z , A, B, C, X, Z ! ' 8 7 7 ( H ' - -+ 7 8
3. A . Z
. A B C X Y Z (. 8 7 $G3 (
10. 3 : +-: P, Q ! ' ( " 2 52 ! I 3 (4:F +3" n (n ! I 3)
+(
Pn(x) = {a0, a1, a2, X, an} , Qn(x) = {b0, b1, b2, X, bn} *+# P Q , an, bn 0 2# 3 "
+ 2 3 " P+Q H P + Q = {ci = ai + bi F3 0 i n | ai P, bi Q} -+ 7 8 3,7 a2+
3. ' P + Q ! ' 3+
. :" I 3 i -+. 8 7 33 7 n 8+ 7 ai + bi ! I 3
. :" " 2 52 (4:F P2(x) , Q2(x) H a0, a1, a2 , b0, b1, b2 , + $ a1 = a0 + a2
, b0 = b1 + b2 , 8+ 7 2 | c1
(. $G3 F3
2 !
1. 3 : +-: A , B ! ' ( 3K4 4 56 $ ' A 123 6 , ' B 123 3
(: 123 ( ' (A J B) (A B) (5 )
2. 3 : +-: A , B ! ' ( 3K4 4 56 U $ A B ( +( 7 A B = B *+#-1

3. a K 4 6 J # , "6 (5 )
3. 3 : +-: A, B , C ! ' ( 3K4 4 56 U $ A B , B C ( +( 7 A C
*+#-1 a K 4 6 J # , "6 (5 )
4. 3 : +-: A = {x | x ! 4 #G7" : 7 ( 51 , 100}
B = {y | y ! 4 3 8 7 33 7 100},
C = {z | z ! 4 3 8 7 33 7 100 , , *++- :,3 2 ! G7}
(: 123 ( B J (AJ C) (5 )