添加G20260103题目目标
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@ -253977,7 +253977,8 @@
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"objs": [
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"K0103001B",
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"K0103004B",
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"K0101004B"
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"K0101004B",
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"K0103005B"
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],
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"tags": [
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"第一单元"
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@ -268803,7 +268804,8 @@
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"id": "010022",
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"content": "已知集合$A=\\{x, y\\}$, $B=\\{2x, 2x^2\\}$, 且$A=B$. 求集合$A$.",
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"objs": [
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"K0101004B"
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"K0101004B",
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"K0102001B"
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],
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"tags": [
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"第一单元"
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@ -268938,7 +268940,8 @@
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"content": "已知集合$A=\\{x|x=2n+1,\\ n\\in \\mathbf{Z}\\}$, $B=\\{x|x=4n-1,\\ n\\in \\mathbf{Z}\\}$. 判断集合$A$与$B$的包含关系, 并证明你的结论.",
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"objs": [
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"K0103001B",
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"K0103003B"
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"K0103003B",
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"K0103005B"
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],
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"tags": [
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"第一单元",
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@ -313089,7 +313092,10 @@
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"011752": {
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"id": "011752",
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"content": "确定$x$与$y$, 使得集合$\\{2x,x+y\\}=\\{4,8\\}$.",
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"objs": [],
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"objs": [
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"K0102001B",
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"K0101004B"
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],
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"tags": [
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"第一单元"
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],
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@ -313111,7 +313117,11 @@
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"011753": {
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"id": "011753",
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"content": "确定下列每组中两个集合之间的关系:\\\\\n(1) $A=\\{n|n$是$12$的正约数$\\}$, $B=\\{1,2,3,6\\}$;\\\\\n(2) $C=\\{x|-1\\le x< 2\\}$, $D=\\{x|x< 2$或$x>3\\}$;\\\\\n(3) $E=\\{n|n=3k+1,\\ k\\in \\mathbf{N}\\}$, $F=\\{n|n=3m-2,\\ m\\in \\mathbf{N}\\}$.",
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"objs": [],
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"objs": [
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"K0103001B",
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"K0103003B",
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"K0103005B"
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],
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"tags": [
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"第一单元"
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],
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@ -313133,7 +313143,10 @@
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"011754": {
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"id": "011754",
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"content": "写出集合$\\{a,b,c\\}$的所有子集, 并指出哪些是真子集.",
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"objs": [],
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"objs": [
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"K0103001B",
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"K0103005B"
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],
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"tags": [
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"第一单元"
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],
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@ -313155,7 +313168,9 @@
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"011755": {
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"id": "011755",
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"content": "已知集合$A=\\{x|0<x<a\\}$, $B=\\{x|1<x<2\\}$, 若$B\\subseteq A$, 求实数$a$的取值范围.",
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"objs": [],
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"objs": [
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"K0103001B"
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],
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"tags": [
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"第一单元"
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],
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@ -313179,7 +313194,9 @@
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"011756": {
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"id": "011756",
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"content": "已知$A\\subseteq B$, $A\\subseteq C$, $B=\\{0, 2, 4\\}$, $C=\\{0, 2, 6\\}$, 写出所有满足上述条件的集合$A$.",
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"objs": [],
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"objs": [
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"K0103001B"
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],
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"tags": [
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"第一单元"
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],
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@ -313201,7 +313218,9 @@
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"011757": {
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"id": "011757",
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"content": "已知$A=\\{x|x=a+\\sqrt 2b,\\ a,b\\in \\mathbf{N}\\}$, 若集合$B=\\{x|x=\\sqrt 2x_1,\\ x_1\\in A\\}$, 证明: $B\\subset A$.",
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"objs": [],
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"objs": [
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"K0103005B"
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],
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"tags": [
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"第一单元"
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],
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@ -510004,7 +510023,8 @@
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"content": "下列说法正确的有\\blank{50}.\\\\\n\\textcircled{1} 若$a\\in A$且$A\\subseteq B$, 则$a\\in B$; \\textcircled{2} 若$A\\subseteq B$且$A\\subseteq C$, 则$B=C$; \\textcircled{3} 若$A\\subset B$且$B\\subseteq C$, 则$A\\subset C$.",
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"objs": [
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"K0103004B",
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"K0103005B"
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"K0103005B",
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"K0103001B"
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],
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"tags": [
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"第一单元"
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@ -510149,7 +510169,9 @@
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"id": "020028",
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"content": "已知集合$A=\\{1\\}$, $B=\\{x|x\\subseteq A\\}$, 用列举法表示集合$B$. 并指出$A$与$B$的关系.",
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"objs": [
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"K0102001B"
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"K0102001B",
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"K0103001B",
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"K0101001B"
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],
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"tags": [
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"第一单元",
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@ -510203,7 +510225,8 @@
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"id": "020030",
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"content": "设常数$a\\in \\mathbf{R}$. 若集合$A=(-\\infty ,5)$与$B=(-\\infty ,a]$满足$A\\subseteq B$, 则$a$的取值范围是\\blank{50}.\\\\\n证明: $1^\\circ$ 当$a$\\blank{50}时, 任取$x\\in A$, 则\\blank{50}, 所以$x\\in B$, 即$A\\subseteq B$.\\\\ \n$2^\\circ$ 当$a$\\blank{50}时, 取$x_1=$\\blank{50}, 则\\blank{50}, 所以$x_1\\in A$且$x_1\\not \\in B$.\\\\\n由$1^\\circ$、$2^\\circ$可得结论.",
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"objs": [
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"K0103001B"
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"K0103001B",
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"K0103005B"
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],
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"tags": [
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"第一单元",
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