1.
2
.


2(1)x∈Ax∈BA⊆BA⊆B AB
∅
A≠B
(2)U(A∩B)
{(xy)|x1y2}{1,2}
{y|yx2}{x|yx2}{(xy)|yx2}
“apple”15
ABAB
12
{y|yx2}{y|y≥0}{x|yx2}R(){(xy)|yx2}yx2
24115()
A{}B{}A∪BZABZ.


2(P14,7)U{x∈N|0<x≤10}A{1,2,3,4,5,9}B{4,6,7,8,10}A∩B________A∪B________(UA)∪(UB)________(UA)∩(UB)________.
{4}U{1,2,3,5,6,7,8,9,10}∅
A{1,3,5} B{1,2,3,4,5}
C{7,9} D{2,4}


4(2010·)A{x|1≤x≤2}B{x|x1}A∩(RB)( )
A{x|x1} B{x|x≥1}
C{x|1x≤2} D{x|1≤x≤2}
D





1 (1)P{x|xeq \f(1,6)k∈Z}Q{x|xeq \f(k,6)eq \f(1,3)k∈Z}( )
APQ BPQ
CPQ DP∩Q∅


B
(2)(09·)Aeq \b\lc\{\rc\}(\a\vs4\al\co1(x|log2x≤ 2))B(∞a)A⊆Ba(c∞)c________.


A{y|y>0}B{x|1≤x≤1}
∴A∩B{x|0<x≤1}C.
C
(2)A{y|y3x1}B{x|yeq \r(1x2)}A∩B( )
A∅ B[1,0)
(2)ABAy3x1Byeq \r(1x2)


A
A3 B4
C7 D8
x2011xeq \r(2011){2011eq \r(2011)}2213


D
(2)Aeq \b\lc\{\rc\}(\a\vs4\al\co1(x|y\r(x)1))Beq \b\lc\{\rc\}(\a\vs4\al\co1(y|yx2x1))A∩B( )
A.eq \b\lc\{\rc\}(\a\vs4\al\co1(0113)) BR
C(0∞) D[eq \f(3,4)∞)
A{x|x≥0}Beq \b\lc\{\rc\}(\a\vs4\al\co1(y|yx\f(1,2)2\f(3,4)))eq \b\lc\{\rc\}(\a\vs4\al\co1(y|y≥\f(3,4)))A∩B[eq \f(3,4)∞)
(2)Aeq \b\lc\{\rc\}(\a\vs4\al\co1(x|y\r(x)1))Beq \b\lc\{\rc\}(\a\vs4\al\co1(y|yx2x1))A∩B( )
A.eq \b\lc\{\rc\}(\a\vs4\al\co1(0113)) BR
C(0∞) D[eq \f(3,4)∞)
A{x|x≥0}Beq \b\lc\{\rc\}(\a\vs4\al\co1(y|yx\f(1,2)2\f(3,4)))eq \b\lc\{\rc\}(\a\vs4\al\co1(y|y≥\f(3,4)))A∩B[eq \f(3,4)∞)



A{3,5}B⊆AB{x|ax10}B∅a0B≠∅a≠0eq \f(1,a)3eq \f(1,a)5aeq \f(1,3)eq \f(1,5).a{0eq \f(1,3)eq \f(1,5)}{0}{eq \f(1,5)}{eq \f(1,3)}{0eq \f(1,5)}{0eq \f(1,3)}{eq \f(1,5)eq \f(1,3)}


B


B⊆Am21m22m1
m21m1m1
m1A{1,33}B{3,1}B⊆A
m22m1m1m1.




2 (1)(2010·)P{x|x<4}Q{x|x2<4}( )
AP⊆Q BQ⊆P
CP⊆RQ DQ⊆RP
Q{x|2<x<2}Q⊆P.
B


4


(3)M{x|xa0}N{x|ax10}M∩NNa( )
A1 B1
D



3 (1)(2010·)A{x||x|≤1x∈R}B{y|yx2x∈R}A∩B( )
A{x|1≤x≤1} B{x|x≥0}
C{x|0≤x≤1} D∅
A{x||x|≤1}{x|1≤x≤1}B{y|yx2x∈R}{y|y≥0}A∩B{x|0≤x≤1}
C


AA⊆C BC⊆A
CA≠C DA∅
A




b1c21c±ixy∈Sxy∈Scidicidibcd1.
B


(2)()


3 (1)(2010·)ABU{1,3,5,7,9}A∩B{3}(UB)∩A{9}A( )
A{1,3} B{3,7,9}
C{3,5,9} D{3,9}
D


(2)AB________
A∩BA∩(UB)B∩(UA)U(A∪B)(UB)∩(UA)


(3)ABA@Bxy∈RA{x|0≤x≤2}B{y|y3xx0}A@B( )
A{x|0x2}
B{x|1x≤2}
C{x|0≤x≤1x≥2}
D{x|0≤x≤1x2}

A@BA∪BA∩BB{y|y1}A@B{x|0≤x≤1x2}
D




113“”“”
23“”


3
A⊆B⇔A∩BA⇔A∪BB⇔CUA⊇CUB⇔A∩CUB∅.
4
1(2011·)fx→x2ABB{1,2}A∩B( )
A∅ B{1}
D


2(2011·)A{x|x≥1}B{x|x2≤4}A∩B________.
{x|1≤x≤2}
B{x|2≤x≤2}∴A∩B{x|1≤x≤2}


3UZP{x|x2nn∈Z}Q{x|x4mm∈Z}U( )
AP∪Q B(UP)∪Q
CP∪(UQ) D(UP)∪(UQ)
C


(1)(2)(3)(4)
(1)(2)(3)(4)


5(2010·)U{0,1,2,3}A{x∈U|x2mx0}UA{1,2}m________.
3






1(2010·)A{1,1,3}B{a2a24}A∩B{3}a________
1
a243a23a1a1∴a1.


2(2010·)U{1,2,3,4,5}M{1,4}N{1,3,5}N∩(UM)( )
A{1,3} B{1,5}
C{3,5} D{4,5}
B
M{x|2≤x1≤2}{x|1≤x≤3}N{1,3,5…}∴M∩N{1,3}2


4(2010·)SCxy∈Sxyxyxy∈SSS{abi|abi}S0∈SSS⊆T⊆CT________()

abxy∈Sxyxyxyxy0∈SS{0}S{0}⊆TT{0,1}T.


A(UA)∪BU
B(UA)∪(UB)U



6A{x|x28x150}B{x|ax10}B⊆Aa
x2011x2011
{20112011} 2
2
k
6

(k2)
k∈Z∴{x|x2k1k∈Z}{x|xk2k∈Z}
∴PQB.
x
x
2
x
2






2






M
c4.
a≠0a





22AB
3(09·)URM










N
(Venn)
A{3,5}B⊆AB{x|ax1
0}B∅a0B≠∅a≠0

1
a
3
1
a