1.设全集U={3,2a-1,a^2-a+2},若集合A={3,a+2},CuA={8},则实数a的值是__ 2.设A,B,C是三个集合,若A⊆B∪C,则A⊆B或A⊆C.举例说明这命题是假命题.
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![1.设全集U={3,2a-1,a^2-a+2},若集合A={3,a+2},CuA={8},则实数a的值是__ 2.设A,B,C是三个集合,若A⊆B∪C,则A⊆B或A⊆C.举例说明这命题是假命题.](/uploads/image/z/1750478-14-8.jpg?t=1.%E8%AE%BE%E5%85%A8%E9%9B%86U%3D%7B3%2C2a-1%2Ca%5E2-a%2B2%7D%2C%E8%8B%A5%E9%9B%86%E5%90%88A%3D%7B3%2Ca%2B2%7D%2CCuA%3D%7B8%7D%2C%E5%88%99%E5%AE%9E%E6%95%B0a%E7%9A%84%E5%80%BC%E6%98%AF__+2.%E8%AE%BEA%2CB%2CC%E6%98%AF%E4%B8%89%E4%B8%AA%E9%9B%86%E5%90%88%2C%E8%8B%A5A%26%238838%3BB%E2%88%AAC%2C%E5%88%99A%26%238838%3BB%E6%88%96A%26%238838%3BC.%E4%B8%BE%E4%BE%8B%E8%AF%B4%E6%98%8E%E8%BF%99%E5%91%BD%E9%A2%98%E6%98%AF%E5%81%87%E5%91%BD%E9%A2%98.)
1.设全集U={3,2a-1,a^2-a+2},若集合A={3,a+2},CuA={8},则实数a的值是__ 2.设A,B,C是三个集合,若A⊆B∪C,则A⊆B或A⊆C.举例说明这命题是假命题.
1.设全集U={3,2a-1,a^2-a+2},若集合A={3,a+2},CuA={8},则实数a的值是__
2.设A,B,C是三个集合,若A⊆B∪C,则A⊆B或A⊆C.举例说明这命题是假命题.
1.设全集U={3,2a-1,a^2-a+2},若集合A={3,a+2},CuA={8},则实数a的值是__ 2.设A,B,C是三个集合,若A⊆B∪C,则A⊆B或A⊆C.举例说明这命题是假命题.
1.∵全集U={3,2a-1,a²-a+2},集合A={3,a+2},CuA={8},
∴8∈U且8不属于A,
①若2a-1=8,则a=9/2,
此时,全集U={3,8,71/4},集合A={3,13/2},与A是U的子集矛盾,故a=9/2舍去;
②若a²-a+2=8,则a= -2,或a=3
a= -2时,全集U={3,-5,8},集合A={3,0},与A是U的子集矛盾,故a= -2舍去;
a= 3时,全集U={3,5,8},集合A={3,5},CuA={8},∴a= 3,
综上,实数a的值为3.
2.反例:A={1,2},B={0,1},C={2,3}
此时,A包含于B∪C,但A不是B的子集且A不是C的子集.
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