1/5单选题
难度：
1.已知A=
，则有（ ）
，则有（ ） | A |  |
| B |  |
| C |  |
| D |  |
- 提示1：
- IOWFg+e0oOS4jumbhuWQiOS5i+mXtOeahOWFs+ezu+eUqOKAnDxpbWcgd2lkdGg9OSBoZWlnaHQ9MjEgc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC8zMC8yNy9yQkFDRkZQUi1MVGhBNWprQUFBQTdnWVJmQzQwODUucG5nIj7igJ3ooajnpLo=
- 提示2：
- IOWtkOmbhuS5i+mXtOeahOWFs+ezu+eUqOKAnDxpbWcgd2lkdGg9MTAgaGVpZ2h0PTIxIHNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvMzAvMjcvckJBQ0ZGUFItTFNoWURwdUFBQUE1MG1RTzk4NjQxLnBuZyI+4oCd6KGo56S6
正确答案：RA==
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
2/5单选题
难度：
2.给出下列关系：①0 ⊊
；②
；③
⊊
；④
。其中正确的是（ ）
；②；③⊊；④。其中正确的是（ ） | A | ①③ |
| B | ③④ |
| C | ②③ |
| D | ①④ |
- 提示1：
- IDxpbWcgd2lkdGg9OSBoZWlnaHQ9MjEgc3JjPSJodHRwczovL3AxLnFpbmdndW8uY29tL0cxL00wMC82RC81Ri9yQkFDRTFQUi1MVGlyTWxpQUFBQk9uZ2NDbEE2NzEucG5nIj7mmK/ku7vkvZXpm4blkIjnmoTlrZDpm4bvvIzmmK/pnZ7nqbrpm4blkIjnmoTnnJ/lrZDpm4Y=
- 提示2：
- IOKAnDxpbWcgd2lkdGg9OSBoZWlnaHQ9MjEgc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC8zMC8yNy9yQkFDRkZQUi1MVGhBNWprQUFBQTdnWVJmQzQwODUucG5nIj7igJ3ooajnpLrlhYPntKDkuI7pm4blkIjpl7TnmoTlhbPns7s=
- 提示3：
- IOmbhuWQiOaYr+Wug+acrOi6q+eahOWtkOmbhg==
正确答案：Qg==
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
3/5单选题
难度：
3.
已知集合M=
，则集合M的不含元素0的真子集的个数是（ ）
| A | 16 |
| B | 15 |
| C | 8 |
| D | 7 |
- 提示1：
- PHA+5LiN5ZCrMOaXtu+8jOmbhuWQiE3nmoTlhYPntKDmnIkx77yMMu+8jDPlhbEz5LiqPGJyPjwvcD4=
- 提示2：
- PHA+5Luj5YWl5YWs5byPPHNwYW4gY2xhc3M9Im1hdGhxdWlsbC1yZW5kZXJlZC1tYXRoIiBzdHlsZT0iZm9udC1zaXplOjIwcHg7Ij48c3BhbiBjbGFzcz0idGV4dGFyZWEiPjx0ZXh0YXJlYSBkYXRhLWNrZS1lZGl0YWJsZT0iMSIgY29udGVudGVkaXRhYmxlPSJmYWxzZSI+PC90ZXh0YXJlYT48L3NwYW4+PHNwYW4gbWF0aHF1aWxsLWNvbW1hbmQtaWQ9IjkiPjI8L3NwYW4+PHN1cCBjbGFzcz0ibm9uLWxlYWYiIG1hdGhxdWlsbC1jb21tYW5kLWlkPSI2IiBtYXRocXVpbGwtYmxvY2staWQ9IjciPjx2YXIgbWF0aHF1aWxsLWNvbW1hbmQtaWQ9IjEwIj5uPC92YXI+PC9zdXA+PC9zcGFuPjxzcGFuPiZuYnNwOzwvc3Bhbj48YnI+PC9wPg==
正确答案：Qw==
PHA+6Kej5p6Q77ya5LiN5ZCrMOaXtu+8jOmbhuWQiE3nmoTlhYPntKDmnIkx77yMMu+8jDPlhbEz5LiqPGJyPuS7o+WFpeWFrOW8jzxzcGFuIGNsYXNzPSJtYXRocXVpbGwtcmVuZGVyZWQtbWF0aCIgc3R5bGU9ImZvbnQtc2l6ZToyMHB4OyI+PHNwYW4gY2xhc3M9InRleHRhcmVhIj48dGV4dGFyZWEgZGF0YS1ja2UtZWRpdGFibGU9IjEiIGNvbnRlbnRlZGl0YWJsZT0iZmFsc2UiPjwvdGV4dGFyZWE+PC9zcGFuPjxzcGFuIG1hdGhxdWlsbC1jb21tYW5kLWlkPSI5Ij4yPC9zcGFuPjxzdXAgY2xhc3M9Im5vbi1sZWFmIiBtYXRocXVpbGwtY29tbWFuZC1pZD0iNiIgbWF0aHF1aWxsLWJsb2NrLWlkPSI3Ij48dmFyIG1hdGhxdWlsbC1jb21tYW5kLWlkPSIxMCI+bjwvdmFyPjwvc3VwPjwvc3Bhbj48c3Bhbj4gPC9zcGFuPuW+l++8jDxzcGFuIGNsYXNzPSJtYXRocXVpbGwtcmVuZGVyZWQtbWF0aCIgc3R5bGU9ImZvbnQtc2l6ZToyMHB4OyI+PHNwYW4gY2xhc3M9InRleHRhcmVhIj48dGV4dGFyZWEgZGF0YS1ja2UtZWRpdGFibGU9IjEiIGNvbnRlbnRlZGl0YWJsZT0iZmFsc2UiPjwvdGV4dGFyZWE+PC9zcGFuPjxzcGFuIG1hdGhxdWlsbC1jb21tYW5kLWlkPSI5Ij4yPC9zcGFuPjxzdXAgY2xhc3M9Im5vbi1sZWFmIiBtYXRocXVpbGwtY29tbWFuZC1pZD0iNiIgbWF0aHF1aWxsLWJsb2NrLWlkPSI3Ij48c3BhbiBtYXRocXVpbGwtY29tbWFuZC1pZD0iMTEiPjM8L3NwYW4+PC9zdXA+PC9zcGFuPjxzcGFuPiA8L3NwYW4+PTjvvIzljbN7MX3vvIx7Mn3vvIx7M33vvIx7MSwyfe+8jHsxLDN977yMezIsM33vvIx7MSwyLDN977yM56m66ZuGPGJyPuaVhemAiUM8YnI+PC9wPg==
4/5单选题
难度：
4.已知集合A=
，B=
，C=
，D=
，则（ ）
，B=，C=，D=，则（ ） | A |  |
| B |  |
| C |  |
| D |  |
- 提示1：
- IOefqeW9ouOAgeato+aWueW9ouOAgeiPseW9oumDveaYr+W5s+ihjOWbm+i+ueW9og==
- 提示2：
- IOato+aWueW9ouaYr+iPseW9ouaIluefqeW9oueahOS4gOmDqOWIhg==
正确答案：Qg==
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
5/5单选题
难度：
5.集合P=
，Q=
，则P、Q的关系是（ ）
，Q=，则P、Q的关系是（ ） | A | P⊊Q |
| B | Q⊊P |
| C | P=Q |
| D | P、Q无公共元素 |
- 提示1：
- IDxpbWcgd2lkdGg9MTM0IGhlaWdodD00MiBzcmM9Imh0dHBzOi8vcDEucWluZ2d1by5jb20vRzEvTTAwLzZELzY1L3JCQUNFMVBSLVRLeExZUlJBQUFDbFRPT2VGSTIwOS5wbmciPg==
- 提示2：
- IDxpbWcgd2lkdGg9OTggaGVpZ2h0PTQyIHNyYz0iaHR0cHM6Ly9wMS5xaW5nZ3VvLmNvbS9HMS9NMDAvMzAvMkQvckJBQ0ZGUFItVFBSdndrQUFBQUNNejVxSkpBNTc5LnBuZyI+
正确答案：Qw==
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