示范教案( 集合的基本运算第二课时)(8)

示范教案( 集合的基本运算第二课时)

2.∵x2-4x-5=0, ∴x=-1或x=5.

∵A={x|x2-4x-5=0}={-1,5}, 同理,B={-1,1}.

∴A∪B={-1,5}∪{-1,1}={-1,1,5}, A∩B={-1,5}∩{-1,1}={-1}.

3.A∩B={x|x是等腰直角三角形},

A∪B={x|x是等腰三角形或直角三角形}. 4.∵∴A∩(

B={2,4,6},

A={1,3,6,7},

B)={2,4,5}∩{2,4,6}={2,4},

(A)∩(B)={1,3,6,7}∩{2,4,6}={6}. (课本P11习题1.1)

A组

1.(1)∈ (2)∈ (3) (4)∈ (5)∈ (6)∈ 2.(1)∈ (2) (3)∈ 3.(1){2,3,4,5};

(2){-2,1};(3){0,1,2}.

(3)∵-3<2x-1≤3,∴-2<2x≤4. ∴-1<x≤2.

又∵x∈Z,∴x=0,1,2.

∴B={x∈Z|-3<2x-1≤3}={0,1,2}. 4.(1){y|y≥-4}; (2){x|x≠0}; (3){x|x≥

4}. 5

5.(1)∵A={x|2x-3<3x}={x|x>-3},B={x|x≥2}, ∴-4 B,-3 A,{2}B,BA. (2)∵A={x|x2-1=0}={-1,1},

∴1∈A,{-1}A,

A,{1,-1}=A. (3);.

6.∵B={x|3x-7≥8-2x}={x|x≥3},

∴A∪B={x|2≤x<4}∪{x|x≥3}={x|x≥2}, A∩B={x|2≤x<4}∩{x|x≥3}={x|3≤x<4}. 7.依题意,可知A={1,2,3,4,5,6,7,8},

所以A∩B={1,2,3,4,5,6,7,8}∩{1,2,3}={1,2,3}=B, A∩C={1,2,3,4,5,6,7,8}∩{3,4,5,6}={3,4,5,6}=C. 又∵B∪C={1,2,3}∪{3,4,5,6}={1,2,3,4,5,6}.

∴A∩(B∪C)={1,2,3,4,5,6,7,8}∩{1,2,3,4,5,6}={1,2,3,4,5,6}. 又∵B∩C={1,2,3}∩{3,4,5,6}={3},

∴A∪(B∩C)={1,2,3,4,5,6,7,8}∪{3}={1,2,3,4,5,6,7,8}=A.

8.(1)A∪B={x|x是参加一百米跑的同学或参加二百米跑的同学}. (2)A∩C={x|x是既参加一百米跑又参加四百米跑的同学}.